新高考數(shù)學一輪復習講與練第08講 一元函數(shù)的導數(shù)及其應用（二）（練）（原卷版）

第02講一元函數(shù)的導數(shù)及其應用（二）1．已知點SKIPIF1<0在曲線SKIPIF1<0上，則曲線在點SKIPIF1<0處的切線方程為_________.2．過曲線SKIPIF1<0上一點SKIPIF1<0且與曲線在點SKIPIF1<0處的切線垂直的直線的方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．已知曲線SKIPIF1<0與直線SKIPIF1<0相切，則實數(shù)a的值為__________.4．若曲線SKIPIF1<0在SKIPIF1<0處的切線方程為SKIPIF1<0，則SKIPIF1<0__________5、過點SKIPIF1<0作曲線SKIPIF1<0（SKIPIF1<0）的切線，則切點坐標為________．6．已知函數(shù)SKIPIF1<0存在單調(diào)遞減區(qū)間，且SKIPIF1<0的圖象在SKIPIF1<0處的切線l與曲線SKIPIF1<0相切，符合情況的切線l（）A．有3條 B．有2條 C．有1條 D．不存在7．曲線SKIPIF1<0與曲線SKIPIF1<0有（）條公切線.A．1 B．2 C．3 D．48．已知點M在函數(shù)SKIPIF1<0圖象上，點N在函數(shù)SKIPIF1<0圖象上，則SKIPIF1<0的最小值為（）A．1 B．SKIPIF1<0 C．2 D．39．設SKIPIF1<0，當SKIPIF1<0取得最小值SKIPIF1<0時，函數(shù)SKIPIF1<0的最小值為___________.10．若曲線SKIPIF1<0在點SKIPIF1<0處的切線與曲線SKIPIF1<0相切于點SKIPIF1<0，則SKIPIF1<0__________.1．已知曲線SKIPIF1<0在點SKIPIF1<0處的切線的傾斜角為SKIPIF1<0，則SKIPIF1<0的值為（）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．曲線SKIPIF1<0在點SKIPIF1<0處的切線方程是SKIPIF1<0，則切點SKIPIF1<0的坐標是____________.3．已知SKIPIF1<0軸為曲線SKIPIF1<0的切線，則SKIPIF1<0的值為________.4．已知曲線SKIPIF1<0在點SKIPIF1<0處的切線方程為SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知直線SKIPIF1<0是曲線SKIPIF1<0的切線，則實數(shù)SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知函數(shù)SKIPIF1<0，當SKIPIF1<0時，曲線SKIPIF1<0在點SKIPIF1<0與點SKIPIF1<0處的切線總是平行時，則由點SKIPIF1<0可作曲線SKIPIF1<0的切線的條數(shù)為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．無法確定7．若函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0有公切線，則實數(shù)SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．拋物線上的一動點到直線距離的最小值是A． B． C． D．9．已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值為______．10．已知函數(shù)SKIPIF1<0，SKIPIF1<0，若存在SKIPIF1<0使得SKIPIF1<0，則實數(shù)a的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．關于SKIPIF1<0的方程SKIPIF1<0在SKIPIF1<0內(nèi)有且僅有SKIPIF1<0個根，設最大的根是SKIPIF1<0，則SKIPIF1<0與SKIPIF1<0的大小關系是A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．以上都不對1．（2019·全國·高考真題（文））曲線y=2sinx+cosx在點(π，–1)處的切線方程為A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2016·四川·高考真題（文））設直線l1，l2分別是函數(shù)f(x)=SKIPIF1<0圖象上點P1，P-2處的切線，l1與l2垂直相交于點P，且l1，l2分別與y軸相交于點A，B，則△PAB的面積的取值范圍是A．(0,1) B．(0,2) C．(0,+∞) D．(1,+∞)3．（2022·浙江·高考真題）設函數(shù)SKIPIF1<0．(1)求SKIPIF1<0的單調(diào)區(qū)間；(2)已知SKIPIF1<0，曲線SKIPIF1<0上不同的三點SKIPIF1<0處的切線都經(jīng)過點SKIPIF1<0．證明：（?。┤鬝KIPIF1<0，則SKIPIF1<0；（ⅱ）若SKIPIF1<0，則SKIPIF1<0．（注：SKIPIF1<0是自然對數(shù)的底數(shù)）4．（2021·全國·高考真題（理））已知拋物線SKIPIF1<0的焦點為SKIPIF1<0，且SKIPIF1<0與圓SKIPIF1<0上點的距離的最小值為SKIPIF1<0．（1）求SKIPIF1<0；（2）若點SKIPIF1<0在SKIPIF1<0上，SKIPIF1<0是SKIPIF1<0的兩條切線，SKIPIF1<0是切點，求SKIPIF1<0面積的最大值．5．（2017·山東·高考真題（理））已知函數(shù)SKIPIF1<0，SKIPIF1<0，其中SKIPIF1<0是自然對數(shù)的底數(shù).（Ⅰ）求曲線SKIPIF1<0在點SKIPIF1<0處的切線方程；（Ⅱ）令SKIPIF1<0，討論SKIPIF1<0的單調(diào)性并判斷有無極值，有極值時求出極值.6．（2019·全國·高考真題（理））已知函數(shù)SKIPIF1<0.（1）討論f(x)的單調(diào)性，并證明f(x)有且僅有兩個零點；（2）設x0是f(x)的一個零點，證明曲線y=lnx在點A(x0，lnx0)處的切線也是曲線SKIPIF1<0的切線.7．（2010·湖北·高考真題（文））設函數(shù)SKIPIF1<0，其中a＞0，曲線SKIPIF1<0在點P（0，SKIPIF1<0）處的切線方程為y=1（Ⅰ）確定b、c的值（Ⅱ）設曲線SKIPIF1<0在點（SKIPIF1<0）及（SKIPIF1<0）處的切線都過點（0,2）證明：當SKIPIF1<0時，SKIPIF1<0（Ⅲ）若過點（0,2）可作曲線SKIPIF1<0的三條不同切線，求a的取值范圍．8．（2011·陜西·高考真題（理））如圖，從點SKIPIF1<0作SKIPIF1<0軸的垂線交曲線SKIPIF1<0于點SKIPIF1<0，曲線在SKIPIF1<0點處的切線與SKIPIF1<0軸交于點SKIPIF1<0，再從SKIPIF1<0作SKIPIF1<0軸的垂線交曲線于點SKIPIF1<0，依次重復上述過程得到一系列點：SKIPIF1<0，SKIPIF1<0；SKIPIF1<0，SKIPIF1<0；SKIPIF1<0；SKIPIF1<0，SKIPIF1<0記SKIPIF1<0點的坐標為SKIPIF1<0（SKIPIF1<0）（1）試求SKIPIF1<0與SKIPIF1<0的關系（SKIPIF1<0）（2）求SKIPIF1<09．（2015·天津·高考真題（理））已知函數(shù)SKIPIF1<0，其中SKIPIF1<0.（Ⅰ）討論SKIPIF1<0的單調(diào)性；（Ⅱ）設曲線SKIPIF1<0與SKIPIF1<0軸正