2022年导数压轴题题型归纳 .pdf
_ 精品资料导数压轴题题型归纳1.高考命题回顾例 1 已知函数 f(x)exln(x m)(2013 全国新课标卷)(1)设 x0 是 f(x)的极值点,求m,并讨论f(x)的单调性;(2)当 m 2 时,证明f(x)0.例 2 已知函数f(x)x2axb,g(x)ex(cx d),若曲线yf(x)和曲线 yg(x)都过点P(0,2),且在点P处有相同的切线y4x+2(2013 全国新课标卷)()求 a,b,c,d 的值()若 x 2 时,()()f xkg x,求 k 的取值范围。_ 精品资料2.在解题中常用的有关结论(1)曲线()yfx在0 xx处的切线的斜率等于()0fx,且切线方程为000()()()yfxx xf x。(2)若可导函数()yfx在0 xx处取得极值,则0()0fx。反之,不成立。(3)对于可导函数()fx,不等式()fx00的解集决定函数()f x的递增(减)区间。(4)函数()fx在区间 I 上递增(减)的充要条件是:x I()fx0(0)恒成立(()fx不恒为 0).(5)函数()fx(非常量函数)在区间I 上不单调等价于()fx在区间 I 上有极值,则可等价转化为方程()0fx在区间 I 上有实根且为非二重根。(若()fx为二次函数且I=R,则有0)。(6)()fx在区间 I 上无极值等价于()fx在区间在上是单调函数,进而得到()fx0或()fx0在 I 上恒成立(7)若xI,()fx0恒成立,则min()fx0;若x I,()fx0恒成立,则max()fx0(8)若0 xI,使得()0fx0,则max()fx0;若0 xI,使得0()fx0,则min()f x0.(9)设()f x与()g x的定义域的交集为D,若xD()()f xg x恒成立,则有min()()0f xg x.(10)若对11xI、22xI,12()()f xg x恒成立,则minmax()()f xg x.若对11xI,22xI,使得12()()f xg x,则minmin()()f xg x.若对11xI,22xI,使得12()()f xg x,则maxmax()()f xg x.(11)已知()f x在区间1I上的值域为 A,,()g x在区间2I上值域为 B,若对11xI,22xI,使得1()f x=2()g x成立,则AB。(12)若三次函数 f(x)有三个零点,则方程()0fx有两个不等实根12xx、,且极大值大于0,极小值小于0.(13)证题中常用的不等式:ln1(0)xxxln+1(1)xx x()1xex1xexln1(1)12xxxx22ln11(0)22xxxx1xx文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1_ 精品资料3.题型归纳导数切线、定义、单调性、极值、最值、的直接应用例 7(构造函数,最值定位)设函数21xfxxekx(其中kR).()当1k时,求函数fx的单调区间;()当1,12k时,求函数fx在0,k上的最大值M.例 8(分类讨论,区间划分)已知函数3211()(0)32f xxaxxb a,()fx为函数()f x的导函数.(1)设函数 f(x)的图象与x 轴交点为A,曲线 y=f(x)在 A点处的切线方程是33yx,求,a b的值;(2)若函数()()axg xefx,求 函数()g x的单调区间.例 9(切线)设函数.(1)当时,求函数在区间上的最小值;(2)当时,曲线在点处的切线为,与轴交于点求证:.例 10(极值比较)已知函数其中当时,求曲线处的切线的斜率;w.w.w.k.s.5.u.c.o.m 当时,求函数的单调区间与极值.例 11(零点存在性定理应用)已知函数()ln,().xf xx g xe若函数 (x)=f(x),求函数(x)的单调区间;axxf2)(1a)()(xxfxg 1,00a)(xfy)(,(111axxfxPllx)0,(2xAaxx2122()(23)(),xf xxaxaa e xRaR0a()(1,(1)yf xf在点23a()fx11xx+-文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1文档编码:CJ5X4P1D10V2 HV2R2Q7U3G5 ZI5V7K10X8A1_ 精品资料设直线l为函数f(x)的图象上一点A(x0,f(x0)处的切线,证明:在区间(1,+)上存在唯一的x0,使得直线l与曲线y=g(x)相切例12(最值问题,两边分求)已知函数.当时,讨论的单调性;设当时,若对任意,存在,使,求实数取值范围.例13(二阶导转换)已知函数若,求的极大值;若在定义域内单调递减,求满足此条件的实数k的取值范围.例 14(综合技巧)设函数讨论函数的单调性;若有两个极值点,记过点的直线斜率为,问:是否存在,使得?若存在,求出的值;若不存在,请说明理由.1()ln1af 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