【优化探究】2014届高三数学一轮复习 1-2-3第三讲 导数的应用专题检测 新人教A版

letters and calls, a nd do pra ctical thi ngs for the ma sses combi ne good, effective thr oug h reaching people at the s ervice of the "last mile". Third, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Jinping stresse d devel opme nt of innovation forest restr uct uring, revitalizati on of the ol d industrial bases i n Northeast China is the State's maj or strategy, Ce ntral has i ssue d compre hensive opini ons of revit alizing Northea st Chi na and other old i ndustrial bases, t he CPC Ce ntral Committee on revitalization in Nort heast China wer e ... V igorous determi nation does not waver, the work does not sla cken off. Be firm with in the development ha s more to do with hard, a nd not muddl e along, pas sive ina ction. To rely on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only provi des new opportunities for devel opme nt in our region, and gave us new requirements . We must s e ize the opportunit y, full use of nat i onal poli cy, has to be more compli cated, to start a nd target, give full play to t he initiative of leadi ng cadre s at all levels, a ctive, active, focusing on building ne w moment um for development, a ccel erating t ransformation of forest devel opme nt. To im plement th e new development phil os ophy. Phil osophy is t he acti on gui de, new ideas and ne w devel opme nts. Carryi ng out innova tion, coor di nati on a nd development of green, open, s hared i deas, m ust be meas urabl e, dire ct action with new development concept s, training cadres . In a new dev elopment concept as a yardstick. E stablis hed i n line with the new conce pt of evaluation system and evaluati on criteri on, embodies t he new deve lopme nt policy, organi zation, mandate im plementati on, always mea sure d by the new dev elopment philosophy, continuous correcti on of forest trans ition course. I n a ne w devel opme nt conce pt for the pat h command. A s part of the impl ementation of the new devel opme nt philosophy followe d and acti on gui deli nes, firmly adjusted, corre cted and reje ct unsuita ble, ina ppr opriate a nd eve n against the new development i deas, behavi ors and pra ctices , more pragmatic a pproach base d on a broa d visi on, a nd creatively carry out ecologi cal constr uction, i ndustrial devel opme nt, improvi ng pe ople' s livelihood, s uch as the w ork to e nsure t hat new development i deas take root i n forest areas. I n a new development conce pt for weapon traini ng ca dre. Educatio n leaders "in the new, not hing" two arti cles, e nha nci ng vitality and pow er. Combi ned development "six big i ndustry", and im plementation "three big e ngineering", and create "two big envir onment", stre ngthe ning on ne w devel opment , and new economy conce pt of learni ng, and grasp a nd usi ng, real put thought and acti on unified t o new development conce pt up, at wit h new devel opment conce pt armed hims elf, and gui de pra ctice, effective do adv ocate i nnovation, and focused on coor dinati on, a nd a dvocate gree n, a nd thi ck plant ope n, a nd adva nce share d. Second, we must rely on S cience and technology affects. Techni cal innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

导数的应用专题检测 新人教 A 版
一、选择题 1.过点(0,1)且与曲线 y= A.2x-y+1=0 C.x+2y-2=0 解析:因为 y=

x+1 在点(3,2)处的切线垂直的直线的方程为( x-1
B.2x+y-1=0 D.x-2y+2=0

)

x+1 2 2 =1+ ,所以 y′=- 2,从而可知函数在 x=3 处的导 x-1 x-1 (x-1)

1 数值为- ,故所求的直线的斜率是 2,直线方程为 y=2x+1,即 2x-y+1=0. 2 答案:A 2. (2012 年福州模拟)已知 g(x)为三次函数 f(x)= x +ax +cx 的导函数, 则函数 g(x) 3 与 f(x)的图象可能是( )

a

3

2

解析:因为 f′(x)=ax +2ax+c,所以函数 f′(x)的对称轴为 x=-1,故可排除 B, C; 由 A 中 f′(x)的图象知 c=0,所以 f(x)= x +ax =x ( x+a),因此三次函数 f(x)= 3 3

2

a

3

2

2

a

a
3

x3+ax2+cx 只有两个零点,而图象 A 中 f(x)的图象与 x 轴有三个交点,故排除 A.应选 D.
答案:D 1 2 3.(2012 年高考辽宁卷)函数 y= x -ln x 的单调递减区间为( 2 A.(-1,1] C.[1,+∞) B.(0,1] D.(0,+∞) )

1 解析:由题意知,函数的定义域为(0,+∞),又由 y′=x- ≤0,解得 0<x≤1,所以

x

函数的单调递减区间为(0,1]. 答案:B 2 4.(2012 年高考陕西卷)设函数 f(x)= +ln x,则(

x

)

livelihood, i s related to people's w ell-being a nd s oci al harmony and stabilit y. We need t o prote ct and im prove the liv elihood of the people as the starting point and e ndi ng poi nt of transition and improve fore st people's feeli ng and ha ppi ness . To promote poverty relief and devel opme nt work. Im pl ementing poverty al leviation cr ucial proje ct is a major strategi c de cision made by the CPC Central Committee, is also determine d by the provi ncial "f irst proj ect", we must unify think ing and acti on to t he requirements of the Ce ntral, provi ncial , resol utely win t he poverty battle. The previ ous pha se I to 18 stations, Tahe, Pine Ridg e research, visite d many of the poor, go, the heavier, more pres sure . For poverty relief a nd development work, we must pay attenti on to it, alway s in mind, graspi ng ha nds, shoul d not be bl indly optim isti c, ther e can be no sla ck. Poverty alleviation and devel opment li es in pre cise, a ccurate. Pre sent, i n order t o find out the re al base of poor people as soon as 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 the basi s of docume nt manageme nt. To firmly establi sh the "poverty reducti on" concept, i ncreas e the inte nsity of res our ce integration, and related fundi ng, with limited funds wisel y. By usi ng a com binati on of employment, e ntrepre neur shi p for pove rty eradication poverty era di cati on, e ducation, poverty allevi ation, medical ai d of poverty means, due t o effects of poli cies , those policie s, ensure the completion of missi on obje ctives for poverty eradicati on for the year. To actively promote the construction of new t owns. In Fe brua ry thi s year, promulgated by the State Council on further prom oting ur bani zation construction of new opi nions, pr opose d to adhere t o t he pe opl e-centere d, four moderni zations synchr onizati on, optimizati on, e col ogy civili zation a nd cult ural heritage of new ur banizati on path wit h Chi nese chara cteristics. Accor ding to district-wide construction of civilize d city a nd the bea utiful countrysi de, furt her strengt heni ng of urban transport, water supply a nd drai nage a nd sew age, waste di sposal ground, underground, s uch as i nfrastructure construction, strive to create a safer and mor e livable e nvironme nt. To actively s eize the full stop a nd opportu nities for poverty alleviation and deve lopme nt, further efforts to i ncrea se forest villages merge, populati on to t he County ( district) Council sites a nd centres conce ntrated in vill ages and tow ns. Combi ned development of ur ban construction and touri sm industries, careful pla nni ng and constr ucti on of a number of suitabl e for reside ntial and farm tour towns and villages, for ming one vill age one product, a feature pattern. Closer to the mas ses. Si nce la st year, our in -de pth impl ementation of the lea ding cadres of grassroots ma sses at w ork, solve t he pr oblems of a large number of pe ople, get the masses give w hol ehearte d support to and prais e, this w ork will carry on, absol utely ca nnot or movement . Grassr oots mass es and ca dres in combi nation with poverty reducti on, combi ned with the stea dy work of

letters and calls, a nd do pra ctical thi ngs for the ma sses combi ne good, effective thr oug h reaching people at the s ervice of the "last mile". Third, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Jinping stresse d devel opme nt of innovation forest restr uct uring, revitalizati on of the ol d industrial bases i n Northeast C hina is the State's maj or strategy, Ce ntral has i ssue d compre hensive opini ons of revitalizing Northea st Chi na and other old i ndust rial bases, t he CPC Ce ntral Committee on revitalization in Nort heast China wer e ... V igorous determi nation does not waver, th e work does not sla cken off. Be firm with in the development ha s more to do with hard, a nd not muddl e along, pas sive ina ction. To rely on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only provi des new opportunities for devel opme nt in o ur region, and gave us new requirements . We must s e ize the opportunit y, full use of nati onal poli cy, has to be more compli cated, to start a nd target, give full play to t he initiative of leadi ng cadre s at all levels, a ctive, active, focusing on building ne w moment um for development, a ccel erating transformation of forest devel opme nt. To im plement the new development phil os ophy. Phil osophy is t he acti on gui de, new ideas and ne w devel opme nts. Carryi ng out innova tion, coor dinati on a nd development of green, open, s hared i deas, m ust be meas urabl e, dire ct action with new development concept s, training cadres . In a new dev elopment concept as a yardstick. E stablis hed i n line with the new conce pt of evaluation system and evaluati on criteri on, embodies t he new deve lopme nt policy, organi zation, mandate im plementati on, always mea sure d by the new dev elopment philosophy, continuous correcti on of forest trans ition course. I n a ne w devel opme nt conce pt for the pat h command. A s part of the impl ementation of the new devel opme nt philosophy followe d and acti on gui deli nes, firmly adjusted, corre cted and reje ct unsuita ble, ina ppr opriate a nd eve n against the new development i deas, behavi ors and pra ctices , more pragmatic a pproach base d on a broa d visi on, a nd creatively carry out ecologi cal constr uction, i ndustrial devel opme nt, improvi ng pe ople' s livelihood, s uch as the w ork to e nsure t hat new development i deas take root i n forest areas. I n a new development conce pt for weapon traini ng ca dre. Education leaders "in the new, not hing" two art i cles, e nha nci ng vitality and pow er. Combi ned development "six big i ndustry", and im plementation "three big e ngineering", and create "two big envir onment", stre ngthe ning on ne w devel opment , and new economy conce pt of learni ng, and grasp a nd usi ng, real put thought and acti on unified t o new development conce pt up, at wit h new devel opment conce pt armed hims elf, and gui de pra ctice, effective do adv ocate i nnovation, and focused on coor dinati on, a nd a dvocate gree n, a nd thi ck plant ope n, a nd adva nce share d. Second, we must rely on S cience and technology affects. Techni cal innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

1 A.x= 为 f(x)的极大值点 2 1 B.x= 为 f(x)的极小值点 2 C.x=2 为 f(x)的极大值点 D.x=2 为 f(x)的极小值点 解析:利用导数法求解. 2 2 1 ∵f(x)= +ln x(x>0),∴f′(x)=- 2+ .

x

x

x

由 f′(x)=0 解得 x=2. 当 x∈(0,2)时,f′(x)<0,f(x)为减函数; 当 x∈(2,+∞)时,f′(x)>0,f(x)为增函数. ∴x=2 为 f(x)的极小值点. 答案:D 1-x 1 5.(2012 年淄博一检)已知 a≤ +ln x 对任意 x∈[ ,2]恒成立,则 a 的最大值为 x 2 ( ) A.0 C.2 1-x 解析:设 f(x)= +ln x, B.1 D.3

x

-x+x-1 1 x-1 则 f′(x)= + = 2 . 2

x

x

x

1 1 当 x∈[ ,1)时,f′(x)<0,故函数 f(x)在[ ,1)上单调递减; 2 2 当 x∈(1,2]时,f′(x)>0,故函数 f(x)在(1,2]上单调递增, ∴f(x)min=f(1)=0,∴a≤0,即 a 的最大值为 0. 答案:A 二、填空题 1 4 6. 如果曲线 y=x -x 在点 P 处的切线垂直于直线 y=- x, 那么点 P 的坐标为________. 3 解析:由 y′=4x -1,得当 y′=3 时, 有 4x -1=3,可解得 x=1, 此时 P 点的坐标为(1,0) 答案:(1,0) 1 2 x 7.设函数 f(x)=x(e -1)- x ,则函数 f(x)的单调增区间为________. 2
livelihood, i s related to people's w ell-being a nd s oci al harmony and stabilit y. We need t o prote ct and im prove the liv elihood of the people as the starting point and e ndi ng poi nt of transition and improve fore st people's feeli ng and ha ppi ness . To promote poverty relief and devel opme nt work. Im pl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisio n made by the CPC Central Committee, is also determine d by the provi ncial "first proj ect", we must unify think ing and acti on to t he requirements of the Ce ntral, provi ncial , resol utely win t he poverty battle. The previ ous pha se I to 18 stations, Tahe, Pine Ridg e research, visite d many of the poor, go, the heavier, more pres sure . For poverty relief a nd development work, we must pay attenti on to it, alway s in mind, graspi ng ha nds, shoul d not be bl indly optimisti c, ther e can be no sla ck. Poverty alleviation an d devel opment li es in pre cise, a ccurate. Pre sent, i n order t o find out the real base of poor people as soon as 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 the basi s of docume nt manageme nt. To firmly establi sh the "poverty reducti on" concept, i ncreas e the inte nsity of res our ce integration, and related fundi ng, with limited funds wisel y. By usi ng a com bina ti on of employment, e ntrepre neur shi p for pove rty eradication poverty era dicati on, e ducation, poverty allevi ation, medical ai d of poverty means, due t o effects of poli cies , those policie s, ensure the completion of missi on obje ctives for poverty eradicati on for the year. To actively promote the construction of new t owns. In Fe bruary thi s year, promulgated by the State Council on furth er prom oting ur bani zation construction of new opi nions, pr opose d to adhere to t he pe opl e-centere d, four moderni zations synchr onizati on, optimizati on, e col ogy civili zation a nd cult ural heritage of new ur banizati on path wit h Chi nese chara cteristics. Accor di ng to district-wide construction of civilize d city a nd the bea utiful countrysi de, furt her strengt heni ng of urban transport, water supply a nd drai nage a nd sew age, waste di sposal ground, underground, s uch as i nfrastructure construction, strive to create a safer and mor e livable e nvironme nt. To actively s eize the full stop a nd opportunities for poverty alleviation and deve lopme nt, further efforts to i ncrea se forest villages merge, populati on to t he County (district) Council sites a nd centres conce ntrated in vill ages and tow ns. Combi ned development of ur ban construction and touri sm industries, careful pla nni ng and constr ucti on of a n umber of suitabl e for reside ntial and farm tour towns and villages, for ming one vill age one product, a feature pattern. Closer to t he mas ses. Si nce la st year, our in -de pth impl ementation of the lea ding cadres of grassroots ma sses at w ork, solve t he pr oblems of a large number of pe ople, get the masses give w hol ehearte d support to and prais e, this w ork will carry on, absol utely ca nnot or movement . Grassr oots mass es and ca dres in combi nation with poverty reducti on, combi ned

3

3

with the stea dy work of

2

letters and calls, a nd do pra ctical thi ngs for the ma sses combi ne good, effective thr oug h reaching people at the s ervice of the "last mile". Third, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Jinping stresse d devel opme nt of innovation forest restr uct uring, revitalizati on of the ol d industrial bases i n Northeast China is the State's maj or strategy, Ce ntral has i ssue d compre hensive opini ons of revitalizing Northea st Chi na and other old i ndustrial bases, t he CPC Ce ntral Committee on revitalization in Nort heast China wer e ... V igorous determi nation does not waver, the work do es not sla cken off. Be firm with in the development ha s more to do with hard, a nd not muddl e along, pas sive ina ction. To rely on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only provi des new opportunities for devel opme nt in our region, and gave us new requirements . We must s e ize the opportunit y, full use of nati onal poli cy, has to be more compli cated, to start a nd target, give full play to t he initiative of leadi ng cadre s at all levels, a ctive, active, focusing on building ne w moment um for development, a ccel erating transformation of forest devel opme nt. To im plement the new development phil os ophy. Phil osophy is t he acti on gui de, new ideas and ne w devel opme nts. Carryi ng out innova tion, coor dinati on a nd development of green, open, s hared i deas, m ust be meas urabl e, dire ct action with new development concept s, training cadres . In a new dev elopment concept as a yardstick. E stablis hed i n line with the new conce pt of evaluation system and evaluati on criteri on, embodies t he new deve lopme nt policy, organi zation, mandate im plementati on, always mea sure d by the new dev elopment philosophy, continuous correcti on of forest trans ition course. I n a ne w devel opme nt conce pt for the pat h command. A s part of the impl ementation of the new devel opme nt philosophy followe d and acti on gui deli nes, firmly adjusted, corre cted and reje ct unsuita ble, ina ppr opriate a nd eve n against the new development i deas, behavi ors and pra ctices , more pragmatic a pproach base d on a broa d visi on, a nd creatively carry out ecologi cal constr uction, i ndustrial devel opme nt, improvi ng pe ople' s livelihood, s uch as the w ork to e nsure t hat new development i deas take root i n f orest areas. I n a new development conce pt for weapon traini ng ca dre. Education leaders "in the new, not hing" two arti cles, e nha nci ng vitality and pow er. Combi ned development "six big i ndustry", and im plementation "three big e ngineering", and create "two big envir onment", stre ngthe ning on ne w devel opment , and new economy conce pt of learni ng, and grasp a nd usi ng, real put thought and acti on unified t o new development conce pt up, at wit h new devel opment conce pt armed hims elf, and gui de pra ctice, effective do adv ocate i nnovation, and focused on coor dinati on, a nd a dvocate gree n, a nd thi ck plant ope n, a nd adva nce share d. Second, we must rely on S cience and technology affects. Techni cal innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

1 2 x 解析:因为 f(x)=x(e -1)- x , 2 所以 f′(x)=e -1+xe -x=(e -1)·(x+1). 令 f′(x)>0,即(e -1)(x+1)>0, 解得 x∈(-∞,-1)或 x∈(0,+∞). 所以函数 f(x)的单调增区间为(-∞,-1]和[0,+∞). 答案:(-∞,-1]和[0,+∞) 8.已知函数 f(x)=ax +bx +cx,其导函数 y=f′(x)的图象经过点(1,0),(2,0), 如图所示,则下列说法中不正确的是________.
3 2

x

x

x

x

3 ①当 x= 时函数取得极小值; 2 ②f(x)有两个极值点; ③当 x=2 时函数取得极小值; ④当 x=1 时函数取得极大值. 解析:从图象上可以看到:当 x∈(0,1)时,f′(x)>0; 当 x∈(1,2)时,f′(x)<0; 当 x∈(2,+∞)时,f′(x)>0,所以 f(x)有两个极值点 1 和 2,且当 x=2 时函数取得 极小值, 当 x=1 时函数取得极大值.只有①不正确. 答案:① 三、解答题 9.(2012 年益阳模拟)已知函数 f(x)=ln(e +a)(a 为常数)是 R 上的奇函数. (1)求 a 的值; (2)讨论函数 y= ln x 2 -x +2ex-m 的零点的个数. f(x)
x x

解析:(1)因为 f(x)=ln(e +a)是奇函数, 所以 ln(e +a)=-ln(e +a), 所以(e +a)(e +a)=1, 所以 a(e +e +a)=0,所以 a=0. (2)由已知得 ln x ln x 2 = =x -2ex+m, f(x) x
x
-x -x -x

x

x

livelihood, i s related to people's w ell-being a nd s oci al harmony and stabilit y. We need t o prote ct and im prove the liv elihood of the people as the starting point and e ndi ng poi nt of transition and improve fore st people's feeli ng and ha ppi ness . To promote poverty relief and devel opme nt work. Im pl ementing poverty alleviation cr ucial proje ct is a major strategi c de cision made by the CPC Central Comm ittee, is also determine d by the provi ncial "first proj ect", we must unify think ing and acti on to t he requirements of the Ce ntral, provi ncial , resol utely win t he poverty battle. The previ ous pha se I to 18 stations, Tahe, Pine Ridg e research, visite d many of the poor, go, the heavier, more pres sure . For poverty relief a nd development work, we must pay attenti on to it, alway s in mind, g raspi ng ha nds, shoul d not be bl indly optimisti c, ther e can be no sla ck. Poverty alleviation and devel opment li es in pre cise, a ccurate. Pre sent, i n order t o find out the real base of poor people as soon as 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 the basi s of docume nt manageme nt. To firmly establi sh the "poverty reducti on" concept, i ncreas e the inte nsity of res our ce integration, and related fundi ng, with limited funds wisel y. By usi ng a com binati on of employment, e ntrepre neur shi p for pove rty eradication poverty era dicati on, e ducation, poverty allevi ation, medical ai d of poverty means, due t o effects of poli cies , those policie s, ensure the completion of missi on obje ctives for poverty eradicati on for the year. To actively promote the construction of new t owns. In Fe bruary thi s year, promulgated by the State Council on further prom oting ur bani zation construction of new opi nions, pr opose d to adhere to t he pe opl e-centere d, four moderni zations synchr onizati on, optimizati on, e col ogy civili zation a nd cult ural heritage of new ur banizati on path wit h Chi nese chara cteristics. Accor ding to district-wide construction of civilize d city a nd the bea utiful countrysi de, furt her strengt heni ng of urban transport, water supply a nd drai nage a nd sew age, waste di sposal ground, underground, s uch as i nfrastructure construction, strive to create a safer and mor e livable e nvironme nt. To actively s eize the full stop a nd opportunities for poverty alleviation and deve lopme nt, further efforts to i ncrea se forest vi llages merge, populati on to t he County (district) Council sites a nd centres conce ntrated in vill ages and tow ns. Combi ned development of ur ban construction and touri sm industries, careful pla nni ng and constr ucti on of a number of suitabl e for reside ntial and farm tour towns and villages, for ming one vill age one product, a feature pattern. Closer to the mas ses. Si nce la st year, our in-de pth impl ementation of the lea ding cadres of grassroots ma sses at w ork, solve t he pr oblems of a large number of pe ople, get th e masses give w hol ehearte d support to and prais e, this w ork will carry on, absol utely ca nnot or movement . Grassr oots mass es a nd ca dres in combi nation with poverty reducti on, combi ned

with the stea dy work of

3

letters and calls, a nd do pra ctical thi ngs for the ma sses combi ne good, effective thr oug h reaching people at the s ervice of the "last mile". Third, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Jinping stresse d devel opme nt of innovation forest restr uct uring, revitalizati on of the ol d industrial bases i n Northeast C hina is the State's maj or strategy, Ce ntral has i ssue d compre hensive opini ons of revitalizing Northea st Chi na and other old i ndust rial bases, t he CPC Ce ntral Committee on revitalization in Nort heast China wer e ... V igorous determi nation does not waver, th e work does not sla cken off. Be firm with in the development ha s more to do with hard, a nd not muddl e along, pas sive ina ction. To rely on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only provi des new opportunities for devel opme nt in o ur region, and gave us new requirements . We must s e ize the opportunit y, full use of nati onal poli cy, has to be more compli cated, to start a nd target, give full play to t he initiative of leadi ng cadre s at all levels, a ctive, active, focusing on building ne w moment um for development, a ccel erating transformation of forest devel opme nt. To im plement the new development phil os ophy. Phil osophy is t he acti on gui de, new ideas and ne w devel opme nts. Carryi ng out innova tion, coor dinati on a nd development of green, open, s hared i deas, m ust be meas urabl e, dire ct action with new development concept s, training cadres . In a new dev elopment concept as a yardstick. E stablis hed i n line with the new conce pt of evaluation system and evaluati on criteri on, embodies t he new deve lopme nt policy, organi zation, mandate im plementati on, always mea sure d by the new dev elopment philosophy, continuous correcti on of forest trans ition course. I n a ne w devel opme nt conce pt for the pat h command. A s part of the impl ementation of the new devel opme nt philosophy followe d and acti on gui deli nes, firmly adjusted, corre cted and reje ct unsuita ble, ina ppr opriate a nd eve n against the new development i deas, behavi ors and pra ctices , more pragmatic a pproach base d on a broa d visi on, a nd creatively carry out ecologi cal constr uction, i ndustrial devel opme nt, improvi ng pe ople' s livelihood, s uch as the w ork to e nsure t hat new development i deas take root i n forest areas. I n a new development conce pt for weapon traini ng ca dre. Education leaders "in the new, not hing" two art i cles, e nha nci ng vitality and pow er. Combi ned development "six big i ndustry", and im plementation "three big e ngineering", and create "two big envir onment", stre ngthe ning on ne w devel opment , and new economy conce pt of learni ng, and grasp a nd usi ng, real put thought and acti on unified t o new development conce pt up, at wit h new devel opment conce pt armed hims elf, and gui de pra ctice, effective do adv ocate i nnovation, and focused on coor dinati on, a nd a dvocate gree n, a nd thi ck plant ope n, a nd adva nce share d. Second, we must rely on S cience and technology affects. Techni cal innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

ln x 2 令 f1(x)= ,f2(x)=x -2ex+m,

x

1-ln x 因为 f1′(x)= ,当 x∈(0,e)时,f1′(x)>0, 2

x

所以 f1′(x)在(0,e]上为增函数; 当 x∈[e,+∞)时,f1′(x)≤0, 所以 f1(x)在[e,+∞)上为减函数. 1 所以当 x=e 时,[f1(x)]max=f1(e)= , e
2 2 2 1 而 f2(x)=(x-e) +m-e ,所以当 m-e > , e

1 2 即 m>e + 时,所求函数零点的个数为 0; e 1 1 2 2 当 m-e = ,即 m=e + 时, e e 所求函数零点的个数为 1; 1 2 1 2 当 m-e < ,即 m<e + 时, e e 所求函数零点的个数为 2. 10.已知函数 f(x)=x -aln x(a∈R). (1)若 a=2,求证:f(x)在(1,+∞)上是增函数; (2)求 f(x)在[1,e]上的最小值. 解析:(1)证明:当 a=2 时,f(x)=x -2ln x, 2(x -1) 当 x∈(1,+∞)时,f′(x)= >0,
2 2 2

x

所以 f(x)在(1,+∞)上是增函数. 2x - a (2)f′(x)= (x>0),
2

x

当 x∈[1,e]时,2x -a∈[2-a,2e -a]. 若 a≤2,则当 x∈[1,e]时,f′(x)≥0,所以 f(x)在[1,e]上是增函数, 又 f(1)=1,故函数 f(x)在[1,e]上的最小值为 1. 若 a≥2e ,则当 x∈[1,e]时,f′(x)≤0, 所以 f(x)在[1,e]上是减函数, 又 f(e)=e -a,所以 f(x)在[1,e]上的最小值为 e -a. 若 2<a<2e ,则当 1≤x<
2 2 2 2

2

2

a

时,f′(x)<0,此时 f(x)是减函数; 2

livelihood, i s related to people's w ell-being a nd s oci al harmony and stabilit y. We need t o prote ct and im prove the liv elihood of the people as the starting point and e ndi ng poi nt of transition and improve fore st people's feeli ng and ha ppi ness . To promote poverty relief and devel opme nt work. Im pl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisio n made by the CPC Central Committee, is also determine d by the provi ncial "first proj ect", we must unify think ing and acti on to t he requirements of the Ce ntral, provi ncial , resol utely win t he poverty battle. The previ ous pha se I to 18 stations, Tahe, Pine Ridg e research, visite d many of the poor, go, the heavier, more pres sure . For poverty relief a nd development work, we must pay attenti on to it, alway s in mind, graspi ng ha nds, shoul d not be bl indly optimisti c, ther e can be no sla ck. Poverty alleviation an d devel opment li es in pre cise, a ccurate. Pre sent, i n order t o find out the real base of poor people as soon as 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 the basi s of docume nt manageme nt. To firmly establi sh the "poverty reducti on" concept, i ncreas e the inte nsity of res our ce integration, and related fundi ng, with limited funds wisel y. By usi ng a com bina ti on of employment, e ntrepre neur shi p for pove rty eradication poverty era dicati on, e ducation, poverty allevi ation, medical ai d of poverty means, due t o effects of poli cies , those policie s, ensure the completion of missi on obje ctives for poverty eradicati on for the year. To actively promote the construction of new t owns. In Fe bruary thi s year, promulgated by the State Council on furth er prom oting ur bani zation construction of new opi nions, pr opose d to adhere to t he pe opl e-centere d, four moderni zations synchr onizati on, optimizati on, e col ogy civili zation a nd cult ural heritage of new ur banizati on path wit h Chi nese chara cteristics. Accor di ng to district-wide construction of civilize d city a nd the bea utiful countrysi de, furt her strengt heni ng of urban transport, water supply a nd drai nage a nd sew age, waste di sposal ground, underground, s uch as i nfrastructure construction, strive to create a safer and mor e livable e nvironme nt. To actively s eize the full stop a nd opportunities for poverty alleviation and deve lopme nt, further efforts to i ncrea se forest villages merge, populati on to t he County (district) Council sites a nd centres conce ntrated in vill ages and tow ns. Combi ned development of ur ban construction and touri sm industries, careful pla nni ng and constr ucti on of a n umber of suitabl e for reside ntial and farm tour towns and villages, for ming one vill age one product, a feature pattern. Closer to t he mas ses. Si nce la st year, our in -de pth impl ementation of the lea ding cadres of grassroots ma sses at w ork, solve t he pr oblems of a large number of pe ople, get the masses give w hol ehearte d support to and prais e, this w ork will carry on, absol utely ca nnot or movement . Grassr oots mass es and ca dres in combi nation with poverty reducti on, combi ned

with the stea dy work of

4

letters and calls, a nd do pra ctical thi ngs for the ma sses combi ne good, effective thr oug h reaching people at the s ervice of the "last mile". Third, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Jinping stresse d devel opme nt of innovation forest restr uct uring, revitalizati on of the ol d industrial bases i n Northeast China is the State's maj or strategy, Ce ntral has i ssue d compre hensive opini ons of revitalizing Northea st Chi na and other old i ndustrial bases, t he CPC Ce ntral Committee on revitalization in Nort heast China wer e ... V igorous determi nation does not waver, the work do es not sla cken off. Be firm with in the development ha s more to do with hard, a nd not muddl e along, pas sive ina ction. To rely on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only provi des new opportunities for devel opme nt in our region, and gave us new requirements . We must s e ize the opportunit y, full use of nati onal poli cy, has to be more compli cated, to start a nd target, give full play to t he initiative of leadi ng cadre s at all levels, a ctive, active, focusing on building ne w moment um for development, a ccel erating transformation of forest devel opme nt. To im plement the new development phil os ophy. Phil osophy is t he acti on gui de, new ideas and ne w devel opme nts. Carryi ng out innova tion, coor dinati on a nd development of green, open, s hared i deas, m ust be meas urabl e, dire ct action with new development concept s, training cadres . In a new dev elopment concept as a yardstick. E stablis hed i n line with the new conce pt of evaluation system and evaluati on criteri on, embodies t he new deve lopme nt policy, organi zation, mandate im plementati on, always mea sure d by the new dev elopment philosophy, continuous correcti on of forest trans ition course. I n a ne w devel opme nt conce pt for the pat h command. A s part of the impl ementation of the new devel opme nt philosophy followe d and acti on gui deli nes, firmly adjusted, corre cted and reje ct unsuita ble, ina ppr opriate a nd eve n against the new development i deas, behavi ors and pra ctices , more pragmatic a pproach base d on a broa d visi on, a nd creatively carry out ecologi cal constr uction, i ndustrial devel opme nt, improvi ng pe ople' s livelihood, s uch as the w ork to e nsure t hat new development i deas take root i n f orest areas. I n a new development conce pt for weapon traini ng ca dre. Education leaders "in the new, not hing" two arti cles, e nha nci ng vitality and pow er. Combi ned development "six big i ndustry", and im plementation "three big e ngineering", and create "two big envir onment", stre ngthe ning on ne w devel opment , and new economy conce pt of learni ng, and grasp a nd usi ng, real put thought and acti on unified t o new development conce pt up, at wit h new devel opment conce pt armed hims elf, and gui de pra ctice, effective do adv ocate i nnovation, and focused on coor dinati on, a nd a dvocate gree n, a nd thi ck plant ope n, a nd adva nce share d. Second, we must rely on S cience and technology affects. Techni cal innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

当 又 f(

a
2

<x≤e 时,f′(x)>0,此时 f(x)是增函数.

a

)= - ln , 2 2 2 2

a a

a

所以 f(x)在[1,e]上的最小值为 - ln . 2 2 2 综上可知,当 a≤2 时,f(x)在[1,e]上的最小值为 1; 当 2<a<2e 时,f(x)在[1,e]上的最小值为
2

a a

a

a a
2

- ln ; 2 2
2 2

a

当 a≥2e 时,f(x)在[1,e]上的最小值为 e -a. 11.已知函数 f(x)=ln x-

a(x-1) . x+1

(1)若函数 f(x)在(0,+∞)上为单调增函数,求 a 的取值范围;

m-n m+n (2)设 m,n∈(0,+∞),且 m≠n,求证: < . ln m-ln n 2
1 a(x+1)-a(x-1) 解析:(1)f′(x)= - 2 x (x+1) (x+1) -2ax x +(2-2a)x+1 = = . x(x+1)2 x(x+1)2 因为 f(x)在(0,+∞)上为单调增函数,所以
2 2

f′(x)≥0 在(0,+∞)上恒成立,即 x2+(2-2a)x+1≥0 在(0,+∞)上恒成立,
当 x∈(0,+∞)时,由 x +(2-2a)x+1≥0,得 1 2a-2≤x+ .
2

x

1 设 g(x)=x+ ,x∈(0,+∞),

x x

1 则 g(x)=x+ ≥2

x· =2, x

1

1 当且仅当 =x,即 x=1 时等号成立,

x

所以 2a-2≤2,即 a≤2, 所以 a 的取值范围是(-∞,2].

m m -1 +1 n n (2)不妨设 m>n.则原不等式等价于 < , m 2 ln n

livelihood, i s related to people's w ell-being a nd s oci al harmony and stabilit y. We need t o prote ct and im prove the liv elihood of the people as the starting point and e ndi ng poi nt of transition and improve fore st people's feeli ng and ha ppi ness . To promote poverty relief and devel opme nt work. Im pl ementing poverty alleviation cr ucial proje ct is a major strategi c de cision made by the CPC Central Comm ittee, is also determine d by the provi ncial "first proj ect", we must unify think ing and acti on to t he requirements of the Ce ntral, provi ncial , resol utely win t he poverty battle. The previ ous pha se I to 18 stations, Tahe, Pine Ridg e research, visite d many of the poor, go, the heavier, more pres sure . For poverty relief a nd development work, we must pay attenti on to it, alway s in mind, g raspi ng ha nds, shoul d not be bl indly optimisti c, ther e can be no sla ck. Poverty alleviation and devel opment li es in pre cise, a ccurate. Pre sent, i n order t o find out the real base of poor people as soon as 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 the basi s of docume nt manageme nt. To firmly establi sh the "poverty reducti on" concept, i ncreas e the inte nsity of res our ce integration, and related fundi ng, with limited funds wisel y. By usi ng a com binati on of employment, e ntrepre neur shi p for pove rty eradication poverty era dicati on, e ducation, poverty allevi ation, medical ai d of poverty means, due t o effects of poli cies , those policie s, ensure the completion of missi on obje ctives for poverty eradicati on for the year. To actively promote the construction of new t owns. In Fe bruary thi s year, promulgated by the State Council on further prom oting ur bani zation construction of new opi nions, pr opose d to adhere to t he pe opl e-centere d, four moderni zations synchr onizati on, optimizati on, e col ogy civili zation a nd cult ural heritage of new ur banizati on path wit h Chi nese chara cteristics. Accor ding to district-wide construction of civilize d city a nd the bea utiful countrysi de, furt her strengt heni ng of urban transport, water supply a nd drai nage a nd sew age, waste di sposal ground, underground, s uch as i nfrastructure construction, strive to create a safer and mor e livable e nvironme nt. To actively s eize the full stop a nd opportunities for poverty alleviation and deve lopme nt, further efforts to i ncrea se forest vi llages merge, populati on to t he County (district) Council sites a nd centres conce ntrated in vill ages and tow ns. Combi ned development of ur ban construction and touri sm industries, careful pla nni ng and constr ucti on of a number of suitabl e for reside ntial and farm tour towns and villages, for ming one vill age one product, a feature pattern. Closer to the mas ses. Si nce la st year, our in-de pth impl ementation of the lea ding cadres of grassroots ma sses at w ork, solve t he pr oblems of a large number of pe ople, get th e masses give w hol ehearte d support to and prais e, this w ork will carry on, absol utely ca nnot or movement . Grassr oots mass es a nd ca dres in combi nation with poverty reducti on, combi ned

with the stea dy work of

5

letters and calls, a nd do pra ctical thi ngs for the ma sses combi ne good, effective thr oug h reaching people at the s ervice of the "last mile". Third, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Jinping stresse d devel opme nt of innovation forest restr uct uring, revitalizati on of the ol d industrial bases i n Northeast C hina is the State's maj or strategy, Ce ntral has i ssue d compre hensive opini ons of revitalizing Northea st Chi na and other old i ndust rial bases, t he CPC Ce ntral Committee on revitalization in Nort heast China wer e ... V igorous determi nation does not waver, th e work does not sla cken off. Be firm with in the development ha s more to do with hard, a nd not muddl e along, pas sive ina ction. To rely on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only provi des new opportunities for devel opme nt in o ur region, and gave us new requirements . We must s e ize the opportunit y, full use of nati onal poli cy, has to be more compli cated, to start a nd target, give full play to t he initiative of leadi ng cadre s at all levels, a ctive, active, focusing on building ne w moment um for development, a ccel erating transformation of forest devel opme nt. To im plement the new development phil os ophy. Phil osophy is t he acti on gui de, new ideas and ne w devel opme nts. Carryi ng out innova tion, coor dinati on a nd development of green, open, s hared i deas, m ust be meas urabl e, dire ct action with new development concept s, training cadres . In a new dev elopment concept as a yardstick. E stablis hed i n line with the new conce pt of evaluation system and evaluati on criteri on, embodies t he new deve lopme nt policy, organi zation, mandate im plementati on, always mea sure d by the new dev elopment philosophy, continuous correcti on of forest trans ition course. I n a ne w devel opme nt conce pt for the pat h command. A s part of the impl ementation of the new devel opme nt philosophy followe d and acti on gui deli nes, firmly adjusted, corre cted and reje ct unsuita ble, ina ppr opriate a nd eve n against the new development i deas, behavi ors and pra ctices , more pragmatic a pproach base d on a broa d visi on, a nd creatively carry out ecologi cal constr uction, i ndustrial devel opme nt, improvi ng pe ople' s livelihood, s uch as the w ork to e nsure t hat new development i deas take root i n forest areas. I n a new development conce pt for weapon traini ng ca dre. Education leaders "in the new, not hing" two art i cles, e nha nci ng vitality and pow er. Combi ned development "six big i ndustry", and im plementation "three big e ngineering", and create "two big envir onment", stre ngthe ning on ne w devel opment , and new economy conce pt of learni ng, and grasp a nd usi ng, real put thought and acti on unified t o new development conce pt up, at wit h new devel opment conce pt armed hims elf, and gui de pra ctice, effective do adv ocate i nnovation, and focused on coor dinati on, a nd a dvocate gree n, a nd thi ck plant ope n, a nd adva nce share d. Second, we must rely on S cience and technology affects. Techni cal innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

2( -1) n m 即 ln > , n m +1

m

n

2( -1) n m 即 ln - >0. n m +1

m

n

2(x-1) 设 h(x)=ln x- ,这个函数即为 a=2 时的函数 f(x), x+1 由(1)知这个函数在(1,+∞)上是单调增函数, 又 >1,所以 h( )>h(1)=0, 2( -1) n m 所以 ln - >0, n m +1

m n

m n m

n

m-n m+n 所以 < . ln m-ln n 2

livelihood, i s related to people's w ell-being a nd s oci al harmony and stabilit y. We need t o prote ct and im prove the liv elihood of the people as the starting point and e ndi ng poi nt of transition and improve fore st people's feeli ng and ha ppi ness . To promote poverty relief and devel opme nt work. Im pl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisio n made by the CPC Central Committee, is also determine d by the provi ncial "first proj ect", we must unify think ing and acti on to t he requirements of the Ce ntral, provi ncial , resol utely win t he poverty battle. The previ ous pha se I to 18 stations, Tahe, Pine Ridg e research, visite d many of the poor, go, the heavier, more pres sure . For poverty relief a nd development work, we must pay attenti on to it, alway s in mind, graspi ng ha nds, shoul d not be bl indly optimisti c, ther e can be no sla ck. Poverty alleviation an d devel opment li es in pre cise, a ccurate. Pre sent, i n order t o find out the real base of poor people as soon as 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 the basi s of docume nt manageme nt. To firmly establi sh the "poverty reducti on" concept, i ncreas e the inte nsity of res our ce integration, and related fundi ng, with limited funds wisel y. By usi ng a com bina ti on of employment, e ntrepre neur shi p for pove rty eradication poverty era dicati on, e ducation, poverty allevi ation, medical ai d of poverty means, due t o effects of poli cies , those policie s, ensure the completion of missi on obje ctives for poverty eradicati on for the year. To actively promote the construction of new t owns. In Fe bruary thi s year, promulgated by the State Council on furth er prom oting ur bani zation construction of new opi nions, pr opose d to adhere to t he pe opl e-centere d, four moderni zations synchr onizati on, optimizati on, e col ogy civili zation a nd cult ural heritage of new ur banizati on path wit h Chi nese chara cteristics. Accor di ng to district-wide construction of civilize d city a nd the bea utiful countrysi de, furt her strengt heni ng of urban transport, water supply a nd drai nage a nd sew age, waste di sposal ground, underground, s uch as i nfrastructure construction, strive to create a safer and mor e livable e nvironme nt. To actively s eize the full stop a nd opportunities for poverty alleviation and deve lopme nt, further efforts to i ncrea se forest villages merge, populati on to t he County (district) Council sites a nd centres conce ntrated in vill ages and tow ns. Combi ned development of ur ban construction and touri sm industries, careful pla nni ng and constr ucti on of a n umber of suitabl e for reside ntial and farm tour towns and villages, for ming one vill age one product, a feature pattern. Closer to t he mas ses. Si nce la st year, our in -de pth impl ementation of the lea ding cadres of grassroots ma sses at w ork, solve t he pr oblems of a large number of pe ople, get the masses give w hol ehearte d support to and prais e, this w ork will carry on, absol utely ca nnot or movement . Grassr oots mass es and ca dres in combi nation with poverty reducti on, combi ned

with the stea dy work of

6


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