高考数学解答题专题攻略--2函数与导数

高考数学解答题专题攻略--2函数与导数 高考数学解答题专题攻略--函数与导数 一、08高考 真题 北京中考数学真题pdf四级真题及答案下载历年四级真题下载证券交易真题下载资料分析真题下载 精典回顾: 1.(全国一19)((本小题满分12分) 32a,R已知函数，( fxxaxx()1,，，， (?)讨论函数的单调区间; fx() 21,,(?)设函数在区间内是减函数，求的取值范围( afx(),,，,,33,, 322,解:(1)求导: fxxaxx()1,，，，fxxax()321,，， 2,当时，，，在R上递增 a?3,?0fx()fx()0? 2,,,aa32,当a,3，求得两根为 x,fx()0,3 222,,,,,,,aa3,,,,，,aaaa33在递增，递减， 即，,,，fx(),,,,,,,,333,,,, 2,,,，,aa3递增 ，，,,,,,3,, 2,,,,aa32,?,7,332a?a,3(2)，且解得: ,24,，,aa31,?,,33, 2.(辽宁卷22)((本小题满分14分) lnxfxxx()lnln(1),,，，设函数( 1，x (?)求f(x)的单调区间和极值; (?)是否存在实数a，使得关于x的不等式的解集为(0，+),若存在，求fxa()?,a的取值范围;若不存在，试说明理由( 本小题主要考查函数的导数，单调性，极值，不等式等基础知识，考查综合利用数学知识分 析问题、解决问题的能力(满分14分( 1ln11lnxx,解:(?)( ????????? 2分 fx(),,,，,,22xxxxxx(1)(1)1(1)，，，， ,故当x,(01)，fx()0,时，， ,x,，(1)，?fx()0,时， a year clean government work Conference of the CPC Committee, each quarter a honest analysis of the situation, troubleshoot the independent Commission against corruption risks, develop quality measures. Third, leaders speak low. Team lead told the independent Commission against corruption of the Party Committee of the Party Committee party lectures, lead reporting personal matters related to lead to honest commitment to the officers and men of the whole city, strictly abide by the party discipline and state laws and disciplinary rules of the ICAC against ourselves, behave yourself, to amend and improve themselves, strictly implement sharding bundled packages, contact points responsibility at work, construction and operational work with the deployment, with guidance, and inspection. (B) persistent grasping ideological education leads. A normalized, pay close attention to education. This year, the detachment has launched a "clean" series of education, special education and consolidation of network and information security, through large lecture hall, issued to the officers and men of the ICAC independent Commission against corruption books, visit education base, set warning education activities to further enhance self-discipline consciousness of officers and soldiers. Second, with typical lead. Organizations to carry out a diligent and honest Government advanced units and advanced individuals selected by broad to the third national "ten outstanding fire-guards" Liu Dajing, "" XX's top ten outstanding young persons "in 所以在单调递增，在单调递减( ?????????????? 4分 fx()(1)，?，(01)， 由此知在的极大值为，没有极小值( ????????? 6分 fx()(0)，?，f(1)ln2, a?0(?)(?)当时， ln(1)ln(1)ln，，，,xxxx,,(1)ln(1)ln，，,xxxx由于， fx()0,,,11，，xx 故关于的不等式的解集为(???????????????? 10分 xfxa()?(0)，?， nln21ln1x,,,,na,0(?)当时，由知，其中为nf,，，(2)ln1fx()ln1,，，,,,,nn，1221，xx,,,, 正整数，且有 nn11a,,22( ????????????? 12分 ln11log(1)，,,,,,,,,ene2,,nn222,, nln2ln2ln22ln2nnn?2,,,又时，( nnnn(1),121(11)1，，，,n 2 2ln24ln2a且,,,，n1( nn,12 n4ln22n,，1取整数满足，，且， nn?2ne,,,log(1)00002a nln21aa,,n00则， fa(2)ln1,，，,，,,,nn0012222，,, a,0即当时，关于的不等式的解集不是( xfxa()?(0)，?， 综合(?)(?)知，存在，使得关于的不等式的解集为，且的取axafxa()?(0)，?， ,?，0值范围为( 14分 ，, 3.(江苏卷17)(某地有三家工厂，分别位于矩形ABCD 的顶点A,B 及CD的中点P 处，已知AB=20km,CB =10km ，为了处理三家工厂的污水，现要在矩形ABCD 的区域上(含边界)，且A,B 与等距离的一点O 处建造一个污水处理厂，并铺设排污管道AO,BO,OP ，设排污管 y道的总长为km( a year clean government work Conference of the CPC Committee, each quarter a honest analysis of the situation, troubleshoot the independent Commission against corruption risks, develop quality measures. Third, leaders speak low. Team lead told the independent Commission against corruption of the Party Committee of the Party Committee party lectures, lead reporting personal matters related to lead to honest commitment to the officers and men of the whole city, strictly abide by the party discipline and state laws and disciplinary rules of the ICAC against ourselves, behave yourself, to amend and improve themselves, strictly implement sharding bundled packages, contact points responsibility at work, construction and operational work with the deployment, with guidance, and inspection. (B) persistent grasping ideological education leads. A normalized, pay close attention to education. This year, the detachment has launched a "clean" series of education, special education and consolidation of network and information security, through large lecture hall, issued to the officers and men of the ICAC independent Commission against corruption books, visit education base, set warning education activities to further enhance self-discipline consciousness of officers and soldiers. Second, with typical lead. Organizations to carry out a diligent and honest Government advanced units and advanced individuals selected by broad to the third national "ten outstanding fire-guards" Liu Dajing, "" XX's top ten outstanding young persons "in 高中数学辅导网 PDC(?)按下列 要求 对教师党员的评价套管和固井爆破片与爆破装置仓库管理基本要求三甲医院都需要复审吗 写出函数关系式: ,,?设?BAO=(rad)，将 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 示成的函数关系式; yO ?设OP(km) ，将表示成x的函数关系式( y,xx BA(?)请你选用(?)中的一个函数关系式，确定 污水处理厂的位置，使三条排污管道总长度最短( 【解析】本小题主要考查函数最值的应用( AQ10,(?)?由条件知PQ 垂直平分AB，若?BAO=(rad) ，则, 故 ,,OA,,coscos 101010tan,,,，又OP,10,10ta， ,OB,cos 1010,，，,，，,,所以， yOAOBOP1010tancoscos,, 2010sin,,,,,所求函数关系式为y,，10 0,,,,,cos4,,, 222?若OP=(km) ，则OQ,10,，所以OA =OB= xx101020200,，,,，xxx，， 2yxxxx,，,，,,220200010所求函数关系式为 ，， ,,,,,10coscos2010sin102sin1,,,,, sin，，，，，，'(?)选择函数模型?， y,,22coscos,, 1,,',,,0,,令0 得sin ，因为，所以=， ,y,642 ,,,,,,,'',,yy当时， ，是的减函数;当时， ，是的增函y,0y,00,,,,,,,,,,664,,,, ,,数，所以当=时，。这时点P 位于线段AB 的中垂线上，且距离AB 边 y,，10103min6 103km处。 3 二、09高考数列分析与预测: 以函数为载体，以导数为工具，考查函数性质及导数极值理论，单调性及其应用为目标，是最近几年函数与导数交汇 试题 中考模拟试题doc幼小衔接 数学试题 下载云南高中历年会考数学试题下载N4真题下载党史题库下载 的显著特点和命题趋向，预测2009年高考导数问题命题的五大热点如下: 热点一、在导数与函数性质的交汇点命题:主要考查导数的简单应用，包括求函数的极值，求函数的单调区间，证明函数的单调性等。命题的热点:三次函数求导后为二次函数，结合一元二次方程根的分布，考查代数推理能力、语言转化能力和待定系数法等数学思想。 热点二、在导数与含参数函数的交汇点命题:主要考查含参数函数的极值问题，分类讨论思想及解不等式的能力，利用分离变量法求参数的取值范围等问题。 a year clean government work Conference of the CPC Committee, each quarter a honest analysis of the situation, troubleshoot the京翰教育中心 independent Commission against corruption risks, develop quality measures. Third, leaders speak low. Team lead told the independent Commission against corruption of the Party Committee of the Party Committee party lectures, lead reporting personal matters related to lead to honest commitment to the officers and men of the whole city, strictly abide by the party discipline and state laws and disciplinary rules of the ICAC against ourselves, behave yourself, to amend and improve themselves, strictly implement sharding bundled packages, contact points responsibility at work, construction and operational work with the deployment, with guidance, and inspection. (B) persistent grasping ideological education leads. A normalized, pay close attention to education. This year, the detachment has launched a "clean" series of education, special education and consolidation of network and information security, through large lecture hall, issued to the officers and men of the ICAC independent Commission against corruption books, visit education base, set warning education activities to further enhance self-discipline consciousness of officers and soldiers. Second, with typical lead. Organizations to carry out a diligent and honest Government advanced units and advanced individuals selected by broad to the third national "ten outstanding fire-guards" Liu Dajing, "" XX's top ten outstanding young persons "in 热点三、在导数与解析几何交汇点命题:主要考查对导数的几何意义，切线的斜率，导数与函数单调性，最(极)值等综合运用知识的能力。 热点四、在导数与向量问题交汇点命题:依托向量把函数单调性，奇偶性，解不等式等知识融合在一起。即考查了向量的有关知识，又考查了函数性质及解不等式等 内容 财务内部控制制度的内容财务内部控制制度的内容人员招聘与配置的内容项目成本控制的内容消防安全演练内容 。 热点五、在导数与函数模型构建交汇点命题:主要考查考生将实际问题转化为数学问题，运用导数工具和不等式知识去解决最优化问题的数学应用意识和实践能力。 备考指南: 复习时，考生要“回归”课本，浓缩所学的知识，夯实基础，熟练掌握解题的通性、通法，提高解题速度。同时，许多高考试题在教材中都有原型，即由教材中的例题、习题引申变化而来。因此，考生必须利用好课本，夯实基础知识。 三、高考热点新题: lnx，a1.已知函数 f(x),(a,R)x (?)求的极值; f(x) 2(?)若函数的图象与函数=1的图象在区间上有公共点，求实数a的取f(x)g(x)(0,e] 值范围。 ln(ax)f(x),,ln(ax)，ln(x，1)2.已知函数, (a,0,a,R)x，1 (?)求函数fx()的定义域; (?)求函数fx()的单调区间; aa(?)当fxa()ln(2),>0时，若存在x使得成立，求的取值范围. a year clean government work Conference of the CPC Committee, each quarter a honest analysis of the situation, troubleshoot the independent Commission against corruption risks, develop quality measures. Third, leaders speak low. Team lead told the independent Commission against corruption of the Party Committee of the Party Committee party lectures, lead reporting personal matters related to lead to honest commitment to the officers and men of the whole city, strictly abide by the party discipline and state laws and disciplinary rules of the ICAC against ourselves, behave yourself, to amend and improve themselves, strictly implement sharding bundled packages, contact points responsibility at work, construction and operational work with the deployment, with guidance, and inspection. (B) persistent grasping ideological education leads. A normalized, pay close attention to education. This year, the detachment has launched a "clean" series of education, special education and consolidation of network and information security, through large lecture hall, issued to the officers and men of the ICAC independent Commission against corruption books, visit education base, set warning education activities to further enhance self-discipline consciousness of officers and soldiers. Second, with typical lead. Organizations to carry out a diligent and honest Government advanced units and advanced individuals selected by broad to the third national "ten outstanding fire-guards" Liu Dajing, "" XX's top ten outstanding young persons "in 高中数学辅导网 3.某种商品的成本为5元/ 件，开始按8元/件销售，销售量为50件，为了获得最大利润，商家先后采取了提价与降价两种措施进行试销。经试销发现:销售价每上涨1元每天销售量就减少10件;而降价后，日销售量Q(件)与实际销售价x(元)满足关系: 2 (57),,x39(229107)xx,， Q, 1986,x (78),,xx,5 (1)求总利润(利润,销售额,成本)y(元)与销售价x(件)的函数关系式; (2)试问:当实际销售价为多少元时，总利润最大. 22x，1xcx，，14.已知函数的图像关于原点成中心对称 ，设函数( gx(),fx(),xc，gxx()ln(1)求的单调区间; fx() xmex,(2)已知对任意恒成立(求实数m的取值范围(其中e是自然对数的x,，,(1,) 底数)( a year clean government work Conference of the CPC Committee, each quarter a honest analysis of the situation, troubleshoot the京翰教育中心 independent Commission against corruption risks, develop quality measures. Third, leaders speak low. Team lead told the independent Commission against corruption of the Party Committee of the Party Committee party lectures, lead reporting personal matters related to lead to honest commitment to the officers and men of the whole city, strictly abide by the party discipline and state laws and disciplinary rules of the ICAC against ourselves, behave yourself, to amend and improve themselves, strictly implement sharding bundled packages, contact points responsibility at work, construction and operational work with the deployment, with guidance, and inspection. (B) persistent grasping ideological education leads. A normalized, pay close attention to education. This year, the detachment has launched a "clean" series of education, special education and consolidation of network and information security, through large lecture hall, issued to the officers and men of the ICAC independent Commission against corruption books, visit education base, set warning education activities to further enhance self-discipline consciousness of officers and soldiers. Second, with typical lead. Organizations to carry out a diligent and honest Government advanced units and advanced individuals selected by broad to the third national "ten outstanding fire-guards" Liu Dajing, "" XX's top ten outstanding young persons "in 2f(x),(x,1)，blnxb5.设函数，其中为常数( 1b,(?)当时，判断函数在定义域上的单调性; fx()2 b(?)若函数的有极值点，求的取值范围及的极值点; fx()fx() 11,b,,1(?)若,试利用(II)求证:n3时，恒有。 ,，,,ln1lnnn，，2nn 126.已知函数 fxxgxa()ln(1),().,，,，2x,1 (1) 求在处的切线方程 gx()l;Pg(2,(2)) l(2) 若的一个极值点到直线的距离为1，求的值; afx() (3) 求方程的根的个数. fxgx()(), y 7.某建筑公司要在一块宽大的矩形地面(如图所示)上进行开发建设,阴影部分为一公共设施建设不能开发,且要求用栏栅隔开(栏栅要求在一直线上), N Pa year clean government work Conference of the CPC Committee, each quarter a honest analysis of the situation, troubleshoot the independent Commission against corruption risks, develop quality measures. Third, leaders speak low. Team lead told the independent Commission against corruption of the Party Committee of the Party Committee party lectures, lead reporting personal matters related to lead to honest commitment to the officers and men of the whole city, strictly abide by the party discipline and state laws and disciplinary rules of the ICAC against ourselves, behave yourself, to amend and improve themselves, strictly implement sharding bundled packages, contact points responsibility at work, construction and operational work with the deployment, with guidance, and inspection. (B) persistent grasping ideological education leads. A normalized, pay close attention to education. This year, the detachment has launched a "clean" series of education, special education and consolidation of network and information security, through large lecture hall, issued to the officers and men of the ICAC independent Commission against corruption books, visit education base, set warning education activities to further enhance self-discipline consciousness of officers and soldiers. Second, with typical lead. Organizations to carry out a diligent and honest Government advanced units and advanced individuals selected by broad to the third national "ten outstanding fire-guards" Liu Dajing, "" XX's top ten outstanding young persons "in x MO 高中数学辅导网 2公共设施边界为曲线的一部分,栏栅与矩形区域的边界交于点M、N，fxaxa()1(0),,, 交曲线于点P，设 Ptft(,()) ,OMNS(1)将(O为坐标原点)的面积表示成的函数; St()t 1(2)若在处，取得最小值，求此时的值及的最小值. t,aSt()St()2 四、高考热点新题参考答案: 1,(lnx，a),f(x)的定义域为(0,，,),f(x),1解:(1) 2x 1,a,令 f(x),0得x,e 1,a,当是增函数 x,(0,e)时,f(x),0,f(x) 1,a,当是减函数 x,(e,，,)时,f(x),0,f(x) 1,a1,aa,1f(x)在x,e处取得极大值,f(x),f(e),e? 极大值 1,a21,a1,a2a,,1时e,e(2)(i)当时，，由(?)知上是增函数，在f(x)在(0,e)(e,e]上是减函数 11,,aa？,,fxfee()() max a year clean government work Conference of the CPC Committee, each quarter a honest analysis of the situation, troubleshoot the京翰教育中心 independent Commission against corruption risks, develop quality measures. Third, leaders speak low. Team lead told the independent Commission against corruption of the Party Committee of the Party Committee party lectures, lead reporting personal matters related to lead to honest commitment to the officers and men of the whole city, strictly abide by the party discipline and state laws and disciplinary rules of the ICAC against ourselves, behave yourself, to amend and improve themselves, strictly implement sharding bundled packages, contact points responsibility at work, construction and operational work with the deployment, with guidance, and inspection. (B) persistent grasping ideological education leads. A normalized, pay close attention to education. This year, the detachment has launched a "clean" series of education, special education and consolidation of network and information security, through large lecture hall, issued to the officers and men of the ICAC independent Commission against corruption books, visit education base, set warning education activities to further enhance self-discipline consciousness of officers and soldiers. Second, with typical lead. Organizations to carry out a diligent and honest Government advanced units and advanced individuals selected by broad to the third national "ten outstanding fire-guards" Liu Dajing, "" XX's top ten outstanding young persons "in ,a,a,a2a,1又当时，所以x,e时,f(x),0,当x,(0,e]时f(x),0.当x,(e,e]f(x),(0.e) a,12的图象在上有公共点，等价于 e,1f(x)与图象g(x),1(0,e] 解得 a,1,又a,,1,所以a,1 1,a22e,e即a,,1(ii)当时，上是增函数， f(x)在(0,e] 2，a22? f(x)在(0,e]上的最大值为f(e),2e 2，a2所以原问题等价于 ,1,解得a,e,2.2e ？a,,1又，?无解 a,02解:(?)当时函数的定义域为; fx()(0,，,)a,0当时函数的定义域为 fx()(,1,0) x，1,ln(ax)11x,f(x),,，(?) 2xx，1(x，1) 2(x，1),xln(ax),(x，1)，x(x，1),ln(ax),, 22x(x，1)(x，1) 1,ln0ax,x,令时，得即， fx()0,a 11,,a,0x,(0,)x,，,(,)?当时，时，当时，， fx()0,fx()0,aa 11a,0(0,)(,)，,故当 时，函数的递增区间为，递减区间为 aa ,,,,10a,,,10ax?当时，，所以， fx()0,,,,10a故当时，在上单调递增( fx()x,,(1,0) 11,,a,,1x,,(1,)x,(,0)?当时，若，;若，， fx()0,fx()0,aa 11a,,1(1,),(,0)故当时，的单调递增区间为;单调递减区间为( fx()aa 11a,0(0,)(,)，,(?)因为当时，函数的递增区间为;单调递减区间为 aa 1fa()ln(2),x若存在使得fxa()ln(2),成立，只须， a a year clean government work Conference of the CPC Committee, each quarter a honest analysis of the situation, troubleshoot the independent Commission against corruption risks, develop quality measures. Third, leaders speak low. Team lead told the independent Commission against corruption of the Party Committee of the Party Committee party lectures, lead reporting personal matters related to lead to honest commitment to the officers and men of the whole city, strictly abide by the party discipline and state laws and disciplinary rules of the ICAC against ourselves, behave yourself, to amend and improve themselves, strictly implement sharding bundled packages, contact points responsibility at work, construction and operational work with the deployment, with guidance, and inspection. (B) persistent grasping ideological education leads. A normalized, pay close attention to education. This year, the detachment has launched a "clean" series of education, special education and consolidation of network and information security, through large lecture hall, issued to the officers and men of the ICAC independent Commission against corruption books, visit education base, set warning education activities to further enhance self-discipline consciousness of officers and soldiers. Second, with typical lead. Organizations to carry out a diligent and honest Government advanced units and advanced individuals selected by broad to the third national "ten outstanding fire-guards" Liu Dajing, "" XX's top ten outstanding young persons "in 高中数学辅导网 a,0,aa，，11,即ln()ln2201,,,,,,,aaa ,1aa,,,a1,,2 3解:(1)据题意的 239(229107)(5)...(57)xxxx,，,,, 1986,x {yxx,,,,(5)....................(78)x,5 5010(8)(5)...........(8),,,,xxx,, 3239(239252535)...(57),,，,,,xxxx {,,,,6(33)..................................(78)xx 2,，,,10180650.......................(8)xxx 3257,,x(2)由(1)得:当时， yxxx,,,，,39(239252535)'2 yxxxx,,，,,,234(1342)234(6)(7) '56,,x当时，，为增函数 yfx,()y,0 '67,,x当时，为减函数 yyfx,,0,() x,6当时， fxf()(16)195,,？max 78,,xyx,,,6(33)150,156当时， ，, 2x,8当时， yx,,,，10(9)160 x,9当时，y,160 max x,6综上知:当时，总利润最大，最大值为195 21x，x(),(),gx,fx,4解: (1) 由已知可得C=0, ? xxln ln1x,,,fx(),, 令,得xe,(列表如下: fx()0,2lnx x (0,1) (1,)e(,)e，, - - + ,fx() 单调减 单调减 单调增 fx() fx()(,)e，,(0,1)(1,)e所以的单调增区间为,单调减区间为和 a year clean government work Conference of the CPC Committee, each quarter a honest analysis of the situation, troubleshoot the京翰教育中心 independent Commission against corruption risks, develop quality measures. Third, leaders speak low. Team lead told the independent Commission against corruption of the Party Committee of the Party Committee party lectures, lead reporting personal matters related to lead to honest commitment to the officers and men of the whole city, strictly abide by the party discipline and state laws and disciplinary rules of the ICAC against ourselves, behave yourself, to amend and improve themselves, strictly implement sharding bundled packages, contact points responsibility at work, construction and operational work with the deployment, with guidance, and inspection. (B) persistent grasping ideological education leads. A normalized, pay close attention to education. This year, the detachment has launched a "clean" series of education, special education and consolidation of network and information security, through large lecture hall, issued to the officers and men of the ICAC independent Commission against corruption books, visit education base, set warning education activities to further enhance self-discipline consciousness of officers and soldiers. Second, with typical lead. Organizations to carry out a diligent and honest Government advanced units and advanced individuals selected by broad to the third national "ten outstanding fire-guards" Liu Dajing, "" XX's top ten outstanding young persons "in xxmxmx,lnx,1(2)在两边取对数,得(而(所以 ex,m,lnx 由(1)知当时,(所以( me,x,，,(1,)fxfee()(),, 5解:(1)由题意知，的定义域为， fx()(0,，,) 1122(x,)，b,2b2x,2x，b22 f'(x),2x,2，,, (x,0)xxx 1,b,当时， ，函数在定义域上单调递增( fx()0,fx()(0,，,)？2 1/(2) ?由(?)得，当时，,函数无极值点( fx()0,fx()b,2 1121121,b,b,b,?当时，有两个不同解，, fx()0,x,,x,，1222222 11,2b时，，x,,,0,(0,，,)，舍去？i) b,0122 11,2b, 而x,，,1,(0,，,)222 ,此时 ，随在定义域上的变化情况如下表: xfx()fx() ()x，，,(0,x)x x222 , fx()0 ,， fx()减 极小值 增 11,2bb,0, x,，由此表可知:时，有惟一极小值点， fx()22 1,0,,bii) 当时，0<<1 此时，，随的变化情况如下表: xx,xfx()fx()122 0,x x ()xx， ()x，，, x，，x111222 , fx()00 ,，， fx()增 极大值 减 极小值 增 1,b1120,,bx,,由此表可知:时，有一个极大值和一个极小值点fx()1222 ,b112x,，; 222 11,2bb,0, x,，综上所述:当时，有惟一最小值点; fx()22 11,2b11,2b1x,,x,，0,,b当时，fx()有一个极大值点和一个极小值点 22222 2b,,1(3)由(2)可知当时，函数，此时fx()有惟一极小值点f(x),(x,1),lnx31，x, 2 a year clean government work Conference of the CPC Committee, each quarter a honest analysis of the situation, troubleshoot the independent Commission against corruption risks, develop quality measures. Third, leaders speak low. Team lead told the independent Commission against corruption of the Party Committee of the Party Committee party lectures, lead reporting personal matters related to lead to honest commitment to the officers and men of the whole city, strictly abide by the party discipline and state laws and disciplinary rules of the ICAC against ourselves, behave yourself, to amend and improve themselves, strictly implement sharding bundled packages, contact points responsibility at work, construction and operational work with the deployment, with guidance, and inspection. (B) persistent grasping ideological education leads. A normalized, pay close attention to education. This year, the detachment has launched a "clean" series of education, special education and consolidation of network and information security, through large lecture hall, issued to the officers and men of the ICAC independent Commission against corruption books, visit education base, set warning education activities to further enhance self-discipline consciousness of officers and soldiers. Second, with typical lead. Organizations to carry out a diligent and honest Government advanced units and advanced individuals selected by broad to the third national "ten outstanding fire-guards" Liu Dajing, "" XX's top ten outstanding young persons "in 高中数学辅导网 1，31，3且 x,(0,)时，f'(x),0, f(x)在(0,)为减函数22 141，3？当 n,3 时， 0, 1,1，,,，32n 111 ？恒有 f(1),f(1，)，即恒有 0,,ln(1，)2nnn 1当 3 时恒有ln(1)ln 成立？n,n，,n,2n 1x,1则 h'(x),1,,令函数 h(x),(x,1),lnx (x,0) xx？x,1 时，h'(x),0 ，又h(x)在x,1处连续？x,[1,，,)时h(x)为增函数 1111？n,3 时 1,1， ？h(1，),h(1) 即 ,ln(1，),0nnnn 11？ln(n，1),lnn,ln(1，),nn 11综上述可知 n,3 时恒有 ,ln(n，1),lnn,2nn ,2x''6解:(1) 且 ？gx(),？,,g(2)22ga(2)1,，22(1)x, 故在点处的切线方程为: gx()Pg(2,(2))2250xya，,,, 2x'x,0(2)由fx()0,,得， 2x，1 故仅有一个极小值点，根据题意得: fx()M(0,0) 5，a？,,a2a,,8d,,1 或 3 12hxfxgxxa()()()ln(1),,,，,, (3)令 2x,1 ，，2211xx' hxx()2,，,，,,222222xxxx，,，,1(1)1(1)，， 'x,,，,0,1)(1,) 当时， hx()0,, ' 当x,,,,,,(,1)(1,0)时， hx()0, 因此，hx()在(,1),(1,0),,,,时，hx()单调递减， 在(0,1),(1,)，,hx()时，单调递增. a year clean government work Conference of the CPC Committee, each quarter a honest analysis of the situation, troubleshoot the京翰教育中心 independent Commission against corruption risks, develop quality measures. Third, leaders speak low. Team lead told the independent Commission against corruption of the Party Committee of the Party Committee party lectures, lead reporting personal matters related to lead to honest commitment to the officers and men of the whole city, strictly abide by the party discipline and state laws and disciplinary rules of the ICAC against ourselves, behave yourself, to amend and improve themselves, strictly implement sharding bundled packages, contact points responsibility at work, construction and operational work with the deployment, with guidance, and inspection. (B) persistent grasping ideological education leads. A normalized, pay close attention to education. This year, the detachment has launched a "clean" series of education, special education and consolidation of network and information security, through large lecture hall, issued to the officers and men of the ICAC independent Commission against corruption books, visit education base, set warning education activities to further enhance self-discipline consciousness of officers and soldiers. Second, with typical lead. Organizations to carry out a diligent and honest Government advanced units and advanced individuals selected by broad to the third national "ten outstanding fire-guards" Liu Dajing, "" XX's top ten outstanding young persons "in 又为偶函数，当时，极小值为 x,,(1,1)ha(0)1,,hx()hx() ,， 当时，， 当时， x,,1x,,1hx(),,,hx(),，, 当时，， 当时， x,,,hx(),，,hx(),，,x,，, 故的根的情况为: fxgx()(), 10,,aa,1 当时，即时，原方程有2个根; 10,,aa,1 当时，即时，原方程有3个根; 10,,aa,1 当时，即时，原方程有4个根 2,,2atl7解:(1)，切线的斜率为，切线的方程为 yax,,2yatatxt,,,,,(1)2()？ 22221121,,，，atatatat令得 xt,，,,y,0,222atatat 21，at2222t,0,令,得 ？M(,0)yatatatNat,,，,，？，121,(0,1)2at 22211(1)，，atat2？,MON的面积 Stat()(1),,，,224atat 24222321(1)(31)atatatat，,，,,(2) St(),,2244atat 12,,由,得 ？at,,0,0St()0,310,att,,,得 3a 12,当时, St()0,310,att,,,即 3a 12,当时, St()0,310,0att,,,,即 3a 1 ？,当时有最小值tSt,() 3a 1114t,已知在St()取得最小值处, ,故有,？,,a 2233a 412(1)，,411234at,,,故当时,StS()(),,, min4132234,,32 a year clean government work Conference of the CPC Committee, each quarter a honest analysis of the situation, troubleshoot the independent Commission against corruption risks, develop quality measures. Third, leaders speak low. Team lead told the independent Commission against corruption of the Party Committee of the Party Committee party lectures, lead reporting personal matters related to lead to honest commitment to the officers and men of the whole city, strictly abide by the party discipline and state laws and disciplinary rules of the ICAC against ourselves, behave yourself, to amend and improve themselves, strictly implement sharding bundled packages, contact points responsibility at work, construction and operational work with the deployment, with guidance, and inspection. (B) persistent grasping ideological education leads. A normalized, pay close attention to education. This year, the detachment has launched a "clean" series of education, special education and consolidation of network and information security, through large lecture hall, issued to the officers and men of the ICAC independent Commission against corruption books, visit education base, set warning education activities to further enhance self-discipline consciousness of officers and soldiers. Second, with typical lead. Organizations to carry out a diligent and honest Government advanced units and advanced individuals selected by broad to the third national "ten outstanding fire-guards" Liu Dajing, "" XX's top ten outstanding young persons "in