導(dǎo)數(shù)求切線方程專題訓(xùn)練

1、導(dǎo)數(shù)求切線方程專題練習(xí)一、典型例題一曲線方程和切點(diǎn)坐標(biāo),求切線方程例1、求y = 4T3在點(diǎn)P16,8佻的切線方程.二曲線方程和切點(diǎn)斜率,求切線方程例2、Y =奴,求與直線y = _2x 一4垂直的切線方程.三曲線方程和曲線外一點(diǎn),求切線方程例3、過原點(diǎn)做曲線y=ex的切線,求切線斜率和切線方程.四曲線方程和曲線上一點(diǎn),求過該點(diǎn)的切線方程 例4、求曲線y =3x -x3過點(diǎn)A2,-2的切線方程.二、當(dāng)堂檢測(cè)1.求過曲線y =-x3 +x上過點(diǎn)1,0 的切線方程.2.求經(jīng)過原點(diǎn)且與曲線y=/相切的曲線方程.3. 求過曲線y=1 x3+1 x2上一點(diǎn)(0,0)的切線方程.4. 假設(shè)直線e2x +

2、y -e2 -1 = 0與曲線y =1 -aex相切,求a的值.5曲線y=x33x2+1在點(diǎn)(1,一1)處的切線方程為()6 與直線2x_y+4=0的平行的拋物線y=x2的切線方程是()7求過曲線y =x3 2x上的點(diǎn)(1,1)的切線方程.8 求過點(diǎn)(2,0)且與曲線y=1相切的直線方程.x【2021北京市高考文】 函數(shù)f (x) = ax2+1 (a?0), g(x) = x3+bx.(i)假設(shè)曲線y = f(x)與曲線y=g(x)在它們的交點(diǎn)(1,c)處具有公共切線,求 a, b的值；(n)當(dāng)a =3, b = -9時(shí),假設(shè)函數(shù)f(x)+g(x)在區(qū)間k,2上的最大值為28,求k的取值范圍

3、.【2021北京市高考文】 函數(shù)f (x) = x2+xsin x+cosx.(i)假設(shè)曲線y = f(x)在點(diǎn)(a, f(a)處與直線y=b相切,求a與b的值.(n )假設(shè)曲線y = f(x)與直線y=b有兩個(gè)不同的交點(diǎn),求 b的取值范圍.【2021北京市門頭溝區(qū)一模文】函數(shù)f(x)=,其中 淀R .(I) f(x)在x = 1處的切線與x軸平行,求b的值;(n)求f (x)的單調(diào)區(qū)間16.函數(shù)f(x)的導(dǎo)函數(shù)為f'x),且滿足f(x) = 2xf' (lnx,那么f'(兮()A , eB . 1C. 1D . e.一 .9 23 .17如果曲線y=x +3與y=2x

4、在x =x°處的切線互相垂直,貝U x°= 218、函數(shù)y = f(x)的圖象在點(diǎn)M(1, f(1)處的切線方程是y=】x + 2,那么f (1)+尸(1)=24.219.f(x)=ax +bx +c的圖象經(jīng)過點(diǎn)(0,1),且在x=1處的切線萬程是 y=x 2.求y = f (x)的解析式 一3-_20、設(shè)函數(shù) f(x) =x 3ax+b(a#0).(I)假設(shè)曲線 y = f(x)在點(diǎn)(2, f(x)處與直線y=8相切,求a,b的值;(口)求函數(shù)f (x)的單調(diào)區(qū)間與極值點(diǎn).21 .求過點(diǎn)(2, 0)且與曲線y=【相切的直線的方程.x22.(此題總分值12分)解析式；個(gè)不同的函數(shù)f(x) =ax3 +bx2+(c3a2b)x+d的圖象如下列圖.(I) 求c, d的值；(II) 假設(shè)函數(shù)f (x)在x =2處的切線方程為 3x+y11=0,求函數(shù)f (x