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2015优化方案(高考总复习)新课标 湖北理科第二章第13课时课后达标检测


letters and calls, a nd do pra ctical t hings for t he masse s com bine g ood, effective through rea chi ng pe ople at the servi ce of the "last mile". T hird, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Ji npi ng stresse d devel opme nt of innovation forest restructuring, revitalization of the ol d industrial bases i n Northeast Chi na is the State's maj or strategy, Central ha s iss ued compr ehe nsive opi nions of revitalizi ng Nort heast China and other old i ndustrial ba ses, t he CPC Ce ntral Committee on revitalizati on in Nort heast China w ere ... V igoro us determination does not waver, the w ork does not sl acken off. Be firm with in the devel opment has more t o do with har d, and not muddle al ong, passiv e ina ction. To re ly on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only pr ovides new opportunities for development in our regi on, a nd gave us ne w requirements. We must s eize the opportunity, full use of nationa l policy, ha s to be m ore com plicate d, to start and target, give full play to t he initiative of leadi ng ca dres at all level s, active, active, focusi ng on building new moment um for devel opment , accelerating t ransformation of forest devel opment . To im plement t he ne w devel opme nt philos ophy. Phi los ophy is the action gui de, new ideas a nd new deve lopme nts. Carrying out innov ation, coor dinati on a nd development of green, ope n, s hared i deas, must be mea surabl e, dire ct acti on wit h ne w devel opme nt concepts, trai ning ca dres. In a new development concept a s a yardsti ck. Esta blished i n line w ith the new conce pt of evaluati on system a nd eval uation criteri on, embodies the new devel opment poli cy, organizati on, ma ndate im plementation, always mea sure d by the new devel opment phil os ophy, conti nuous correction of forest transition course. In a new development concept for t he pat h comma nd. A s part of the implementati on of the ne w devel opme nt philosophy followe d and acti on gui deli nes, firmly adj usted, corre cted a nd rej ect uns uitable , ina ppropriate a nd eve n agains t the new devel opment i deas, be haviors a nd practi ces, more pragmatic approa ch base d on a br oad visi on, and creatively carry out e col ogica l construction, industrial devel opme nt, improvi ng pe opl e's liveli hood, such as t he w ork to ensure t hat new devel opment i deas take root in forest area s. I n a new dev elopment concept for wea pon traini ng ca dre. Educati on le a ders "in t he ne w, nothi ng" two articl es, e nha nci ng vitality and power. Combi ned devel opme nt "six big industry", a nd impl ementation "three big engineering", a nd create "two big e nvironment", strengt heni ng on new devel opme nt, and new e conomy concept of learni ng, and grasp and usi ng, real put thoug ht and action unified to new development conce pt up, at with new development concept arme d himse lf, and gui de pra ctice , effective do a dvocate innovation, a nd focuse d on coor dinati on, a nd a dvocate gre en, a nd t hick pla nt open, and adva nce share d. Second, we must rely on Scie nce a nd te chnol ogy affects. Te chnical innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

[基础达标] 一、选择题 1.(2014· 山西省考前适应性训练)若商品的年利润 y(万元)与年产量 x(百万件)的函数关 系式:y=-x3+27x+123(x>0),则获得最大利润时的年产量为( ) A.1 百万件 B.2 百万件 C.3 百万件 D.4 百万件 解析:选 C.依题意得,y′=-3x2+27=-3(x-3)(x+3),当 0<x<3 时,y′>0;当 x>3 时,y′<0.因此,当 x=3 时,该商品的年利润最大,故选 C. 2.从边长为 10 cm×16 cm 的矩形纸板的四角截去四个相同的小正方形, 做成一个无盖 的盒子,则盒子容积的最大值为( ) A.12 cm3 B.72 cm3 3 C.144 cm D.160 cm3 解析: 选 C.设盒子容积为 y cm3, 盒子的高为 x cm, 则 y=(10-2x)(16-2x)x=4x3-52x2 +160x(0<x<5), ∴y′=12x2-104x+160. 20 令 y′=0,得 x=2 或 (舍去), 3 ∴ymax=6×12×2=144(cm3). 1 3.(2014· 宜昌模拟)已知 y=f(x)是奇函数,当 x∈(0,2)时,f(x)=ln x-ax(a> ),当 x∈(- 2 2,0)时,f(x)的最小值为 1,则 a 的值等于( ) 1 1 A. B. 4 3 1 C. D.1 2 1 1 解析:选 D.由题意知,当 x∈(0,2)时,f(x)的最大值为-1.令 f′(x)= -a=0,得 x= , x a 1 当 0<x< 时,f′(x)>0; a 1 当 x> 时,f′(x)<0. a 1 ∴f(x)max=f( )=-ln a-1=-1,解得 a=1. a 4.(2014· 山西诊断)设 D 是函数 y=f(x)定义域内的一个区间,若存在 x0∈D,使 f(x0)= -x0,则称 x0 是 f(x)的一个“次不动点”,也称 f(x)在区间 D 上存在“次不动点”,若函数 5 f(x)=ax2-3x-a+ 在区间[1,4]上存在“次不动点”,则实数 a 的取值范围是( ) 2 1 A.(-∞,0) B.(0, ) 2 1 1 C.[ ,+∞) D.(-∞, ] 2 2 5 解析:选 D.设 g(x)=f(x)+x,依题意,存在 x∈[1,4],使 g(x)=f(x)+x=ax2-2x-a+ = 2 4x-5 4x-5 1 5 0.当 x=1 时, g(1)= ≠0; 当 x≠1 时, 由 ax2-2x-a+ =0 得 a= 2 .记 h(x)= 2 2 2 2?x -1? 2?x -1?

livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl ementing poverty allevi ation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimist ic, t here ca n be no s lack. Poverty alleviati on a nd development li es in pre cise, a ccurate. Pre sent, i n order to find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt managem ent . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding , with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre neurs hip for poverty eradication poverty eradi cati on, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by the State Council on furt her pr omoting urba nization constructi on of new opi nions, propos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nizatio n pat h with Chi nese characteristi cs. A ccor ding t o distri ct-wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (dist ri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one v illage one product, a feature pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted support to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical t hings for t he masse s com bine g ood, effective through rea chi ng pe ople at the servi ce of the "last mile". T hird, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Ji npi ng stresse d devel opme nt of innovation forest restructuring, revitalization of the ol d industrial ba ses i n Northeast Chi na is the State's maj or strategy, Central ha s iss ued compr ehe nsive opi nions of revitalizi ng Nort heast China and other old i ndustrial ba ses, t he CPC Ce ntral Committee on revitalizati on in Nort heast China w ere ... V igorous determination does not waver, the w ork does not sl acken off. Be firm with in the devel opment has more t o do with har d, and not muddle al ong, passiv e ina ction. To re ly on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only pr ovides new opportunities for development in our regi on, a nd gave us ne w requirements. We must s eize the opportunity, full use of national policy, ha s to be m or e com plicate d, to start and target, give full play to t he initiative of leadi ng ca dres at all level s, active, active, focusi ng on b uilding new moment um for devel opment , accelerating transformation of forest devel opment . To im plement t he ne w devel opme nt philos ophy. Phi los ophy is the action gui de, new ideas a nd new deve lopme nts. Carrying out innov ation, coor dinati on a nd development of green, ope n, s hared i deas, must be mea surabl e, dire ct acti on wit h ne w devel opme nt concepts, trai ning ca dres. In a new developm ent concept a s a yardsti ck. Esta blished i n line w ith the new conce pt of evaluati on system a nd eval uation criteri on, embodies the new devel opment poli cy, organizati on, ma ndate im plementation, always mea sure d by the new devel opment phil os ophy, conti nuous correction of forest transition course. In a new development concept for t he pat h comma nd. A s part of the implementati on of the ne w devel opme nt philosophy followe d and acti on gui deli nes, firmly adj usted, corre cted a nd rej ect uns uitable , ina ppropriate a nd eve n agains t the new devel opment i deas, be haviors a nd practi ces, more pragmatic approa ch base d on a br oad visi on, and creatively carry out e col ogica l construction, industrial devel opme nt, improvi ng pe opl e's liveli hood, such as t he w ork to ensure t hat new devel opment i deas take root in forest area s. I n a new dev elopment concept for wea pon traini ng ca dre. Educati on lea ders "in t he ne w, nothi ng" two articl es, e nha nci ng vitality and power. Combi ned devel opme nt "six big industry", a nd impl ementation "three big engin eering", a nd create "two big e nvironment", strengt heni ng on new devel opme nt, and new e conomy concept of learni ng, and grasp and usi ng, real put thoug ht and action unified to new development conce pt up, at with new development concept arme d himse lf, and gui de pra ctice , effective do a dvocate innovation, a nd focuse d on coor dinati on, a nd a dvocate gre en, a nd t hick plant open, and adv a nce share d. Second, we must rely on Scie nce a nd te chnol ogy affects. Te chnical innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

-2x2+5x-2 1 (1<x≤4),则由 h′(x)= =0,得 x=2 或 x= (舍去).当 x∈(1,2)时,h′(x)>0; 2 2 2 ?x -1? 当 x∈(2,4)时,h′(x)<0,即函数 h(x)在(1,2)上是增函数,在(2,4)上是减函数,因此当 x=2 1 1 时,h(x)取得最大值,最大值是 h(2)= ,故满足题意的实数 a 的取值范围是(-∞, ],故 2 2 选 D.
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5 . (2014· 浙江省名校联考 ) 设函数 ht(x) =3tx - 2t2 ,若有且仅有一个正实数 x0,使得 h7(x0)≥ht(x0)对任意的正数 t 都成立,则 x0=( A.5 B. 5 C.3 D. 7
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解析:选 D.∵h7(x0)≥ht(x0)对任意的正数 t 都成立, ∴h7(x0)≥ht(x0)max.记 g(t)=ht(x0)=3tx0-2t2,则 g′(t)=3x0-3t2,令 g′(t)=0,得 t=x2 0,
3 3 易得 ht(x0)max=g(x2 0)=x0,∴21x0-14 7≥x0,将选项代入检验可知选 D. 二、填空题 6.函数 f(x)=ax3+x 恰有三个单调区间,则 a 的取值范围是________. 1

解析:f(x)=ax3+x 恰有三个单调区间,即函数 f(x)恰有两个极值点,即 f′(x)=0 有两 个不等实根. ∵f(x)=ax3+x,∴f′(x)=3ax2+1. 要使 f′(x)=0 有两个不等实根,则 a<0. 答案:(-∞,0) 7. (2014· 广州模拟)设函数 f(x)=ax3-3x+1(x∈R), 若对于任意 x∈[-1,1], 都有 f(x)≥0 成立,则实数 a 的值为________. 解析:(构造法)若 x=0,则不论 a 取何值,f(x)≥0 显然成立; 3 1 当 x>0 时,即 x∈(0,1]时,f(x)=ax3-3x+1≥0 可化为 a≥ 2- 3. x x 3 1 设 g(x)= 2- 3, x x 3?1-2x? 则 g′(x)= , x4 1 1 0, ?上单调递增,在区间? ,1?上单调递减, 所以 g(x)在区间? ? 2? ?2 ? 1 ? 因此 g(x)max=g? ?2?=4,从而 a≥4. 3 1 当 x<0 时,即 x∈[-1,0)时,同理 a≤ 2- 3. x x g(x)在区间[-1,0)上单调递增, ∴g(x)min=g(-1)=4, 从而 a≤4,综上可知 a=4. 答案:4 三、解答题 ln x 8.(2013· 高考北京卷)设 L 为曲线 C:y= 在点(1,0)处的切线. x (1)求 L 的方程; (2)证明:除切点(1,0)之外,曲线 C 在直线 L 的下方.

livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stat ions, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack. Pover ty alleviati on a nd development li es in pre cise, a ccurate. Pre sent, i n order to find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre neurs hip for poverty eradication poverty eradi cation, educati on, poverty all eviatio n, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by the Stat e Council on furt her pr omoting urba nization constructi on of new opi nions, propos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese charact eristi cs. A ccor ding t o distri ct-wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one village one product, a feature pat tern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted support to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical t hings for t he masse s com bine g ood, effective through rea chi ng pe ople at the servi ce of the "last mile". T hird, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Ji npi ng stresse d devel opme nt of innovation forest restructuring, revitalization of the ol d industrial bases i n Northeast Chi na is the State's maj or strategy, Central ha s iss ued compr ehe nsive opi nions of revitalizi ng Nort heast China and other old i ndustrial ba ses, t he CPC Ce ntral Committee on revitalizati on in Nort heast China w ere ... V igorous determination does not waver, the w ork does not sl acken off. Be firm with in the devel opment has more t o do with har d, and not muddle al ong, passiv e ina ction. To re ly on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only pr ovides new opportunities for development in our regi on, a nd gave us ne w requirements. We must s eize the opportunity, full use of national policy, ha s to be m ore com plica te d, to start and target, give full play to t he initiative of leadi ng ca dres at all level s, active, active, focusi ng on building new moment um for devel opment , accelerating transformation of forest devel opment . To im plement t he ne w devel opme nt philos ophy. Phi los ophy is the action gui de, new ideas a nd new deve lopme nts. Carrying out innov ation, coor dinati on a nd development of green, ope n, s hared i deas, must be mea surabl e, dire ct acti on wit h ne w devel opme nt concepts, trai ning ca dres. In a new development concept a s a yardsti ck. Esta blished i n line w ith the new conce pt of evaluati on system a nd eval uation criteri on, embodies the new devel opment poli cy, organizati on, ma ndate im plementation, always mea sure d by the new devel opment phil os ophy, conti nuous correction of forest transition course. In a new development concept for t he pat h comma nd. A s part of the implementati on of the ne w devel opme nt philosophy followe d and acti on gui deli nes, firmly adj usted, corre cted a nd rej ect uns uitable , ina ppropriate a nd eve n agains t the new devel opment i deas, be haviors a nd practi ces, more pragmatic approa ch base d on a br oad visi on, and creatively carry out e col ogica l construction, industrial devel opme nt, improvi ng pe opl e's liveli hood, such as t he w ork to ensure t hat new devel opment i de as take root in forest area s. I n a new dev elopment concept for wea pon traini ng ca dre. Educati on lea ders "in t he ne w, nothi ng" two articl es, e nha nci ng vitality and power. Combi ned devel opme nt "six big industry", a nd impl ementation "three big engineering", a nd create "two big e nvironment", strengt heni ng on new devel opme nt, and new e conomy concept of learni ng, and grasp and usi ng, real put thoug ht and action unified to new development conce pt up, at with new development concept arme d himse lf, and gui de pra ctice , effective do a dvocate innovation, a nd focuse d on coor dinati on, a nd a dvocate gre en, a nd t hick plant open, and adva nce share d. Second, we must rely on Scie nce a nd te chnol ogy affects. Te chnical innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

1-ln x ln x 解:(1)设 f(x)= ,则 f′(x)= . x x2 所以 f′(1)=1,所以 L 的方程为 y=x-1. (2)证明:令 g(x)=x-1-f(x),则除切点之外,曲线 C 在直线 L 的下方等价于 g(x)>0(? x>0,x≠1). g(x)满足 g(1)=0,且 x2-1+ln x g′(x)=1-f′(x)= . x2 当 0<x<1 时,x2-1<0,ln x<0,所以 g′(x)<0,故 g(x)单调递减; 当 x>1 时,x2-1>0,ln x>0,所以 g′(x)>0,故 g(x)单调递增. 所以,g(x)>g(1)=0(?x>0,x≠1). 所以除切点之外,曲线 C 在直线 L 的下方. 9.(2014· 山东泰安模拟)某种产品每件成本为 6 元,每件售价为 x 元(6<x<11),年销售 585 21 为 u 万件,若已知 -u 与(x- )2 成正比,且售价为 10 元时,年销售为 28 万件. 8 4 (1)求年销售利润 y 关于售价 x 的函数关系式; (2)求售价为多少时,年利润最大,并求出最大年利润. 585 21 解:(1)设 -u=k(x- )2, 8 4 ∵售价为 10 元时,年销量为 28 万件, 585 21 ∴ -28=k(10- )2,解得 k=2. 8 4 21 2 585 ∴u=-2(x- ) + =-2x2+21x+18. 4 8 ∴y=(-2x2+21x+18)(x-6)=-2x3+33x2-108x-108(6<x<11). (2)y′=-6x2+66x-108=-6(x2-11x+18)=-6(x-2)(x-9). 令 y′=0,得 x=2(舍去)或 x=9, 显然,当 x∈(6,9)时,y′>0; 当 x∈(9,11)时,y′<0. ∴函数 y=-2x3+33x2-108x-108 在(6,9)上是单调递增的,在(9,11)上是单调递减的. ∴当 x=9 时,y 取最大值,且 ymax=135, ∴售价为 9 元时,年利润最大,最大年利润为 135 万元. 10.(2014· 黄冈市高三检测)设 f(x)=ex-a(x+1). (1)若 a>0,f(x)≥0 对一切 x∈R 恒成立,求 a 的最大值; a (2)设 g(x)=f(x)+ x,且 A(x1,y1),B(x2,y2)(x1≠x2)是曲线 y=g(x)上任意两点,若对任 e 意的 a≤-1,直线 AB 的斜率恒大于常数 m,求 m 的取值范围; e (3)求证:1n+3n+…+(2n-1)n< (2n)n(n∈N*). e-1 解: (1)因为 f(x)=ex-a(x+1), 所以 f′(x)=ex-a, 因为 a>0,f′(x)=ex-a=0 的解为 x=ln a. 所以 f(x)min=f(ln a)=a-a(ln a+1)

livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relie f a nd development work . Impl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack. Poverty alleviati on a nd development li es in pr e cise, a ccurate. Pre sent, i n order to find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepr e neurs hip for poverty eradication poverty eradi cation, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by the State Council on furt her pr omoting urba nizatio n constructi on of new opi nions, propos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese characteristi cs. A ccor ding t o distri ct-wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dent ial a nd farm tour towns a nd v illages, f orming one village one product, a feature pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted support to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical t hings for t he masse s com bine g ood, effective through rea chi ng pe ople at the servi ce of the "last mile". T hird, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Ji npi ng stresse d devel opme nt of innovation forest restructuring, revitalization of the ol d industrial ba ses i n Northeast Chi na is the State's maj or strategy, Central ha s iss ued compr ehe nsive opi nions of revitalizi ng Nort heast China and other old i ndustrial ba ses, t he CPC Ce ntral Committee on revitalizati on in Nort heast China w ere ... V igorous determination does not waver, the w ork does not sl acken off. Be firm with in the devel opment has more t o do with har d, and not muddle al ong, passiv e ina ction. To re ly on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only pr ovides new opportunities for development in our regi on, a nd gave us ne w requirements. We must s eize the opportunity, full use of national policy, ha s to be m or e com plicate d, to start and target, give full play to t he initiative of leadi ng ca dres at all level s, active, active, focusi ng on b uilding new moment um for devel opment , accelerating transformation of forest devel opment . To im plement t he ne w devel opme nt philos ophy. Phi los ophy is the action gui de, new ideas a nd new deve lopme nts. Carrying out innov ation, coor dinati on a nd development of green, ope n, s hared i deas, must be mea surabl e, dire ct acti on wit h ne w devel opme nt concepts, trai ning ca dres. In a new developm ent concept a s a yardsti ck. Esta blished i n line w ith the new conce pt of evaluati on system a nd eval uation criteri on, embodies the new devel opment poli cy, organizati on, ma ndate im plementation, always mea sure d by the new devel opment phil os ophy, conti nuous correction of forest transition course. In a new development concept for t he pat h comma nd. A s part of the implementati on of the ne w devel opme nt philosophy followe d and acti on gui deli nes, firmly adj usted, corre cted a nd rej ect uns uitable , ina ppropriate a nd eve n agains t the new devel opment i deas, be haviors a nd practi ces, more pragmatic approa ch base d on a br oad visi on, and creatively carry out e col ogica l construction, industrial devel opme nt, improvi ng pe opl e's liveli hood, such as t he w ork to ensure t hat new devel opment i deas take root in forest area s. I n a new dev elopment concept for wea pon traini ng ca dre. Educati on lea ders "in t he ne w, nothi ng" two articl es, e nha nci ng vitality and power. Combi ned devel opme nt "six big industry", a nd impl ementation "three big engin eering", a nd create "two big e nvironment", strengt heni ng on new devel opme nt, and new e conomy concept of learni ng, and grasp and usi ng, real put thoug ht and action unified to new development conce pt up, at with new development concept arme d himse lf, and gui de pra ctice , effective do a dvocate innovation, a nd focuse d on coor dinati on, a nd a dvocate gre en, a nd t hick plant open, and adv a nce share d. Second, we must rely on Scie nce a nd te chnol ogy affects. Te chnical innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

=-aln a, 因为 f(x)≥0 对一切 x∈R 恒成立, 所以-aln a≥0,所以 aln a≤0,所以 amax=1. (2)设 x1、x2 是任意的两实数,且 x1<x2, g?x2?-g?x1? >m,故 g(x2)-mx2>g(x1)-mx1. x2-x1 ∴不妨令函数 F(x)=g(x)-mx,则 F(x)在(-∞,+∞)上单调递增, ∴F′(x)=g′(x)-m>0 恒成立. ∴对任意的 a≤-1,x∈R,m<g′(x)恒成立, a g′(x)=ex-a- x≥2 e 故 m<3.
i ?2n-i? i i (3)证明:由(1)知 ex≥x+1,取 x=- ,i=1,3,…,2n-1,得 1- ≤e-2r,即? ? 2n 2n ? 2n ? n

?- ax?-a=-a+2 ex· ? e?

-a=(

-a+1)2-1≥3,

≤e-2, 累加得, 2n-1?n - ? 1 ?n+? 3 ?n+…+? ? ? ≤e ?2n? ?2n? ? 2n ? ∴1n+3n+…+(2n-1)n< e
2n-1 2 1

i

+e-

2n-3 2

e-2?1-e-n? 1 e +…+e-2= < . 1 - 1-e e-1

(2n)n. e-1

[能力提升] 1.(2014· 浙江省名校联考)已知函数 f(x)=ax-ex(a>0). 1 (1)当 a= 时,求函数 f(x)的单调区间; 2 (2)当 1≤a≤1+e 时,求证:f(x)≤x. 1 1 解:(1)当 a= 时,f(x)= x-ex. 2 2 1 令 f′(x)= -ex=0,得 x=-ln 2. 2 当 x<-ln 2 时,f′(x)>0;当 x>-ln 2 时,f′(x)<0. ∴函数 f(x)的单调递增区间为(-∞,-ln 2),单调递减区间为(-ln 2,+∞). (2)证明:令 F(x)=x-f(x)=ex-(a-1)x. ①当 a=1 时,F(x)=ex>0,∴f(x)≤x 成立; ②当 1<a≤1+e 时,F′(x)=ex-(a-1)=ex-eln(a-1), 当 x<ln(a-1)时,F′(x)<0;当 x>ln(a-1)时,F′(x)>0, ∴F(x)在(-∞,ln(a-1))上单调递减,在(ln(a-1),+∞)上单调递增, ∴F(x)≥F(ln(a-1))=eln(a-1)-(a-1)ln(a-1)=(a-1)[1-ln(a-1)], ∵1<a≤1+e,∴a-1>0,1-ln(a-1)≥1-ln[(1+e)-1]=0, ∴F(x)≥0,即 f(x)≤x 成立. 综上,当 1≤a≤1+e 时,有 f(x)≤x. 2.(2014· 湖北省教学合作联考)已知函数 f(x)=ln x-x+1,x∈(0,+∞).g(x)=x3-ax.
livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stat ions, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack. Pover ty alleviati on a nd development li es in pre cise, a ccurate. Pre sent, i n order to find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre neurs hip for poverty eradication poverty eradi cation, educati on, poverty all eviatio n, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by the Stat e Council on furt her pr omoting urba nization constructi on of new opi nions, propos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese charact eristi cs. A ccor ding t o distri ct-wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one village one product, a feature pat tern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted support to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical t hings for t he masse s com bine g ood, effective through rea chi ng pe ople at the servi ce of the "last mile". T hird, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Ji npi ng stresse d devel opme nt of innovation forest restructuring, revitalization of the ol d industrial bases i n Northeast Chi na is the State's maj or strategy, Central ha s iss ued compr ehe nsive opi nions of revitalizi ng Nort heast China and other old i ndustrial ba ses, t he CPC Ce ntral Committee on revitalizati on in Nort heast China w ere ... V igorous determination does not waver, the w ork does not sl acken off. Be firm with in the devel opment has more t o do with har d, and not muddle al ong, passiv e ina ction. To re ly on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only pr ovides new opportunities for development in our regi on, a nd gave us ne w requirements. We must s eize the opportunity, full use of national policy, ha s to be m ore com plica te d, to start and target, give full play to t he initiative of leadi ng ca dres at all level s, active, active, focusi ng on building new moment um for devel opment , accelerating transformation of forest devel opment . To im plement t he ne w devel opme nt philos ophy. Phi los ophy is the action gui de, new ideas a nd new deve lopme nts. Carrying out innov ation, coor dinati on a nd development of green, ope n, s hared i deas, must be mea surabl e, dire ct acti on wit h ne w devel opme nt concepts, trai ning ca dres. In a new development concept a s a yardsti ck. Esta blished i n line w ith the new conce pt of evaluati on system a nd eval uation criteri on, embodies the new devel opment poli cy, organizati on, ma ndate im plementation, always mea sure d by the new devel opment phil os ophy, conti nuous correction of forest transition course. In a new development concept for t he pat h comma nd. A s part of the implementati on of the ne w devel opme nt philosophy followe d and acti on gui deli nes, firmly adj usted, corre cted a nd rej ect uns uitable , ina ppropriate a nd eve n agains t the new devel opment i deas, be haviors a nd practi ces, more pragmatic approa ch base d on a br oad visi on, and creatively carry out e col ogica l construction, industrial devel opme nt, improvi ng pe opl e's liveli hood, such as t he w ork to ensure t hat new devel opment i de as take root in forest area s. I n a new dev elopment concept for wea pon traini ng ca dre. Educati on lea ders "in t he ne w, nothi ng" two articl es, e nha nci ng vitality and power. Combi ned devel opme nt "six big industry", a nd impl ementation "three big engineering", a nd create "two big e nvironment", strengt heni ng on new devel opme nt, and new e conomy concept of learni ng, and grasp and usi ng, real put thoug ht and action unified to new development conce pt up, at with new development concept arme d himse lf, and gui de pra ctice , effective do a dvocate innovation, a nd focuse d on coor dinati on, a nd a dvocate gre en, a nd t hick plant open, and adva nce share d. Second, we must rely on Scie nce a nd te chnol ogy affects. Te chnical innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

(1)求 f(x)的最大值; (2)若对?x1∈(0,+∞),总存在 x2∈[1,2]使得 f(x1)≤g(x2)成立,求 a 的取值范围; 1?n ?2?n e ?n?n (3)证明不等式:? ?n? +?n? +…+?n? <e-1. 解:(1)因为 f(x)=ln x-x+1(x>0), 1-x 1 所以 f′(x)= -1= , x x 所以当 0<x<1 时,f′(x)>0,x>1 时,f′(x)<0. 所以 f(x)≤f(1)=0.所以 f(x)的最大值为 0. (2)?x1∈(0,+∞),?x2∈[1,2]使得 f(x1)≤g(x2)成立,等价于 f(x)max≤g(x)max. 由(1)知 f(x)max=0,当 a≤0 时,g(x)=x3-ax 在 x∈[1,2)时恒为正,满足题意; 当 a>0 时,g′(x)=3x2-a,令 g′(x)=0,解得 x=± 所以 g(x)在(-∞,- 若 a )及( 3 a ,+∞)上单调递增. 3 a . 3

a ≤1, 即 0<a≤3 时, g(x)max=g(2)=8-2a, 所以 8-2a≥0.所以 a≤4.所以 0<a≤3; 3 a a a 若 1< ≤2,即 3<a≤12 时,g(x)在[1, ]上递减,在[ ,2]上单调递增. 3 3 3 而 g(1)=1-a<0,g(2)=8-2a 在(3,4]为正,在(4,12)为负, 所以 3<a≤4. 当 a >2,即 a>12 时,g(1)<0,g(2)<0 不合题意. 3

综上 a 的取值范围为 a≤4. (3)由(1)知 f(x)≤0,即 ln x≤x-1(x>0). k-n k k k 取 x= ,所以 ln ≤ -1= . n n n n k?n k-n k 所以 nln ≤k-n,即? ?n? ≤e . n 1?n ?2?n ?n?n≤e1-n+e2-n+…+en-n 所以? + + … + ?n? ?n? ?n? e1-n-en-n· e e1-n-e e-e1-n e = = = < . 1-e 1-e e-1 e-1 ln x 3.(2014· 广东韶关阶段检测)已知函数 f(x)=ln x-x,h(x)= . x (1)求 h(x)的最大值; (2)若关于 x 的不等式 xf(x)≥-2x2+ax-12 对一切 x∈(0,+∞)恒成立,求实数 a 的取 值范围; (3)若关于 x 的方程 f(x)-x3+2ex2-bx=0 恰有一解,其中 e 为自然对数的底数,求实数 b 的值. ln x 解:(1)因为 h(x)= (x>0), x 1-ln x 所以 h′(x)= . x2 由 h′(x)>0,且 x>0,得 0<x<e.由 h′(x)<0,且 x>0,得 x>e, 所以函数 h(x)的单调增区间是(0,e],单调减区间是[e,+∞).
livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relie f a nd development work . Impl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack. Poverty alleviati on a nd development li es in pr e cise, a ccurate. Pre sent, i n order to find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepr e neurs hip for poverty eradication poverty eradi cation, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by the State Council on furt her pr omoting urba nizatio n constructi on of new opi nions, propos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese characteristi cs. A ccor ding t o distri ct-wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dent ial a nd farm tour towns a nd v illages, f orming one village one product, a feature pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted support to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical t hings for t he masse s com bine g ood, effective through rea chi ng pe ople at the servi ce of the "last mile". T hird, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Ji npi ng stresse d devel opme nt of innovation forest restructuring, revitalization of the ol d industrial ba ses i n Northeast Chi na is the State's maj or strategy, Central ha s iss ued compr ehe nsive opi nions of revitalizi ng Nort heast China and other old i ndustrial ba ses, t he CPC Ce ntral Committee on revitalizati on in Nort heast China w ere ... V igorous determination does not waver, the w ork does not sl acken off. Be firm with in the devel opment has more t o do with har d, and not muddle al ong, passiv e ina ction. To re ly on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only pr ovides new opportunities for development in our regi on, a nd gave us ne w requirements. We must s eize the opportunity, full use of national policy, ha s to be m or e com plicate d, to start and target, give full play to t he initiative of leadi ng ca dres at all level s, active, active, focusi ng on b uilding new moment um for devel opment , accelerating transformation of forest devel opment . To im plement t he ne w devel opme nt philos ophy. Phi los ophy is the action gui de, new ideas a nd new deve lopme nts. Carrying out innov ation, coor dinati on a nd development of green, ope n, s hared i deas, must be mea surabl e, dire ct acti on wit h ne w devel opme nt concepts, trai ning ca dres. In a new developm ent concept a s a yardsti ck. Esta blished i n line w ith the new conce pt of evaluati on system a nd eval uation criteri on, embodies the new devel opment poli cy, organizati on, ma ndate im plementation, always mea sure d by the new devel opment phil os ophy, conti nuous correction of forest transition course. In a new development concept for t he pat h comma nd. A s part of the implementati on of the ne w devel opme nt philosophy followe d and acti on gui deli nes, firmly adj usted, corre cted a nd rej ect uns uitable , ina ppropriate a nd eve n agains t the new devel opment i deas, be haviors a nd practi ces, more pragmatic approa ch base d on a br oad visi on, and creatively carry out e col ogica l construction, industrial devel opme nt, improvi ng pe opl e's liveli hood, such as t he w ork to ensure t hat new devel opment i deas take root in forest area s. I n a new dev elopment concept for wea pon traini ng ca dre. Educati on lea ders "in t he ne w, nothi ng" two articl es, e nha nci ng vitality and power. Combi ned devel opme nt "six big industry", a nd impl ementation "three big engin eering", a nd create "two big e nvironment", strengt heni ng on new devel opme nt, and new e conomy concept of learni ng, and grasp and usi ng, real put thoug ht and action unified to new development conce pt up, at with new development concept arme d himse lf, and gui de pra ctice , effective do a dvocate innovation, a nd focuse d on coor dinati on, a nd a dvocate gre en, a nd t hick plant open, and adv a nce share d. Second, we must rely on Scie nce a nd te chnol ogy affects. Te chnical innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

1 所以当 x=e 时,h(x)取得最大值 . e (2)因为 xf(x)≥-2x2+ax-12 对一切 x∈(0,+∞)恒成立, 即 xln x-x2≥-2x2+ax-12 对一切 x∈(0,+∞)恒成立, 12 即 a≤ln x+x+ 对一切 x∈(0,+∞)恒成立, x 12 设 φ(x)=ln x+x+ , x x2+x-12 ?x-3??x+4? 因为 φ′(x)= = , x2 x2 故 φ(x)在(0,3]上递减,在[3,+∞)上递增,φ(x)min= φ(3)=7+ln 3, 所以 a≤7+ln 3. 即实数 a 的取值范围是(-∞,7+ln 3]. (3)因为方程 f(x)-x3+2ex2-bx=0 恰有一解, 即 ln x-x-x3+2ex2-bx=0 恰有一解, ln x 即 =x2-2ex+b+1 恰有一解. x 1 由(1)知,h(x)在 x=e 时,h(x)max= , e 而函数 k(x)=x2-2ex+b+1 在(0,e]上单调递减,在[e,+∞)上单调递增, ln x 故 x=e 时,k(x)min=b+1-e2,故方程 =x2-2ex+b+1 恰有一解时当且仅当 b+1 x 1 -e2= , e 1 即 b=e2+ -1. e 4.(2014· 武汉市武昌区训练)设函数 f(x)=xln x. (1)求函数 f(x)的最小值; (2)设 x1,x2>0,p1,p2>0,且 p1+p2=1,证明: p1f(x1)+p2f(x2)≥f(p1x1+p2x2); (3)设 x1,x2,…,xn>0,p1,p2,…,pn>0,且 p1+p2+…+pn=1,如果 p1x1+p2x2 +…+pnxn≥e,证明: p1f(x1)+p2f(x2)+…+pnf(xn)≥e. 解:(1)f′(x)=1+ln x. 1 1 由 f′(x)>0,得 x> ;由 f′(x)<0,得 0<x< . e e 1 1 ∴f(x)在(0, )上单调递减;f(x)在( ,+∞)上单调递增. e e 1 1 1 ? ∴f(x)在 x= 处取最小值 f? ? e?=-e. e (2)证明:令 g(x)=p1f(x1)+p2f(x)-f(p1x1+p2x),不妨设 x1≤x≤x2, 则 g′(x)=p2f′(x)-p2f′(p1x1+p2x). ∵p1x1+p2x-x=p1x1-p1x≤0, ∴p1x1+p2x≤x. 而 f′(x)=1+ln x 是增函数, ∴f′(x)≥f′(p1x1+p2x).
livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stat ions, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack. Pover ty alleviati on a nd development li es in pre cise, a ccurate. Pre sent, i n order to find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre neurs hip for poverty eradication poverty eradi cation, educati on, poverty all eviatio n, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by the Stat e Council on furt her pr omoting urba nization constructi on of new opi nions, propos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese charact eristi cs. A ccor ding t o distri ct-wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one village one product, a feature pat tern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted support to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical t hings for t he masse s com bine g ood, effective through rea chi ng pe ople at the servi ce of the "last mile". T hird, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Ji npi ng stresse d devel opme nt of innovation forest restructuring, revitalization of the ol d industrial bases i n Northeast Chi na is the State's maj or strategy, Central ha s iss ued compr ehe nsive opi nions of revitalizi ng Nort heast China and other old i ndustrial ba ses, t he CPC Ce ntral Committee on revitalizati on in Nort heast China w ere ... V igorous determination does not waver, the w ork does not sl acken off. Be firm with in the devel opment has more t o do with har d, and not muddle al ong, passiv e ina ction. To re ly on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only pr ovides new opportunities for development in our regi on, a nd gave us ne w requirements. We must s eize the opportunity, full use of national policy, ha s to be m ore com plica te d, to start and target, give full play to t he initiative of leadi ng ca dres at all level s, active, active, focusi ng on building new moment um for devel opment , accelerating transformation of forest devel opment . To im plement t he ne w devel opme nt philos ophy. Phi los ophy is the action gui de, new ideas a nd new deve lopme nts. Carrying out innov ation, coor dinati on a nd development of green, ope n, s hared i deas, must be mea surabl e, dire ct acti on wit h ne w devel opme nt concepts, trai ning ca dres. In a new development concept a s a yardsti ck. Esta blished i n line w ith the new conce pt of evaluati on system a nd eval uation criteri on, embodies the new devel opment poli cy, organizati on, ma ndate im plementation, always mea sure d by the new devel opment phil os ophy, conti nuous correction of forest transition course. In a new development concept for t he pat h comma nd. A s part of the implementati on of the ne w devel opme nt philosophy followe d and acti on gui deli nes, firmly adj usted, corre cted a nd rej ect uns uitable , ina ppropriate a nd eve n agains t the new devel opment i deas, be haviors a nd practi ces, more pragmatic approa ch base d on a br oad visi on, and creatively carry out e col ogica l construction, industrial devel opme nt, improvi ng pe opl e's liveli hood, such as t he w ork to ensure t hat new devel opment i de as take root in forest area s. I n a new dev elopment concept for wea pon traini ng ca dre. Educati on lea ders "in t he ne w, nothi ng" two articl es, e nha nci ng vitality and power. Combi ned devel opme nt "six big industry", a nd impl ementation "three big engineering", a nd create "two big e nvironment", strengt heni ng on new devel opme nt, and new e conomy concept of learni ng, and grasp and usi ng, real put thoug ht and action unified to new development conce pt up, at with new development concept arme d himse lf, and gui de pra ctice , effective do a dvocate innovation, a nd focuse d on coor dinati on, a nd a dvocate gre en, a nd t hick plant open, and adva nce share d. Second, we must rely on Scie nce a nd te chnol ogy affects. Te chnical innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

∴g′(x)=p2f′(x)-p2f′(p1x1+p2x)≥0,所以 g(x)在(x1,x2)上是增函数. ∴g(x2)≥g(x1)=0,即 p1f(x1)+p2f(x2)-f(p1x1+p2x2)≥0. ∴p1f(x1)+p2f(x2)≥f(p1x1+p2x2). (3)证明:先证明 p1f(x1)+p2f(x2)+…+pnf(xn)≥f(p1x1+p2x2+…+pnxn). 当 n=2 时,由(2)知不等式成立. 假设当 n=k 时,不等式成立,即 p1f(x1)+p2f(x2)+…+pkf(xk)≥f(p1x1+p2x2+…+pkxk). 当 n=k+1 时,f(p1x1+p2x2+…+pkxk+pk+1xk+1)

? ? ?p1x1+p2x2+…+pkxk? p1x1+p2x2+…+pkxk +pk+1xk+1? ≤(1 - pk + 1)f ? = f ??1-pk+1? ? + pk + 1-pk+1 1-pk+1 ? ? ? ?
1f(xk+1)≤(1-pk+1)

? p1 ? pk +1 p2 f?x1?+ f?x2?+…+ f?xk+1?? ? 1-pk+1 1-pk+1 ?1-pk+1 ?
+pk+1f(xk+1) =p1f(x1)+p2f(x2)+…+pk+1f(xk+1)+pk+1f(xk+1). 所以,当 n=k+1 时,不等式成立, ∴p1f(x1)+p2f(x2)+…+pnf(xn)≥f(p1x1+p2x2+…+pnxn). 1 ? 由(1)知 f(x)在? ?e,+∞?上单调递增,因此 f(x)在(e,+∞)上也单调递增. ∵p1x1+p2x2+…+pnxn≥e, ∴f(p1x1+p2x2+…+pnxn)≥f(e)=e. ∴p1f(x1)+p2f(x2)+…+pnf(xn)≥e.

livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relie f a nd development work . Impl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack. Poverty alleviati on a nd development li es in pr e cise, a ccurate. Pre sent, i n order to find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepr e neurs hip for poverty eradication poverty eradi cation, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by the State Council on furt her pr omoting urba nizatio n constructi on of new opi nions, propos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese characteristi cs. A ccor ding t o distri ct-wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dent ial a nd farm tour towns a nd v illages, f orming one village one product, a feature pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted support to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of



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