新高考數(shù)學(xué)二輪復(fù)習(xí)重難點(diǎn)突破專題25 參變分離法解決導(dǎo)數(shù)問題(原卷版)

專題25參變分離法解決導(dǎo)數(shù)問題一、單選題1．已知函數(shù)SKIPIF1<0SKIPIF1<0，且SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0恒成立，則a的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．若函數(shù)SKIPIF1<0沒有極值點(diǎn)，則實(shí)數(shù)a的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．若函數(shù)SKIPIF1<0在SKIPIF1<0上是減函數(shù)，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知函數(shù)SKIPIF1<0（SKIPIF1<0為自然對(duì)數(shù)的底數(shù)），SKIPIF1<0．若存在實(shí)數(shù)SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0，且SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．15．設(shè)函數(shù)SKIPIF1<0在SKIPIF1<0上有兩個(gè)零點(diǎn)，則實(shí)數(shù)a的取值范圍（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知關(guān)于x的方程SKIPIF1<0在SKIPIF1<0上有兩解，則實(shí)數(shù)k的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．若函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．若關(guān)于x的不等式（a+2）x≤x2+alnx在區(qū)間[SKIPIF1<0，e]（e為自然對(duì)數(shù)的底數(shù)）上有實(shí)數(shù)解，則實(shí)數(shù)a的最大值是（）A．﹣1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．已知函數(shù)SKIPIF1<0，SKIPIF1<0（SKIPIF1<0，SKIPIF1<0為自然對(duì)數(shù)的底數(shù)）.若存在SKIPIF1<0，使得SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知函數(shù)SKIPIF1<0，其中SKIPIF1<0，若對(duì)于任意的SKIPIF1<0，且SKIPIF1<0，都有SKIPIF1<0SKIPIF1<0成立，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．已知函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則實(shí)數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<013．對(duì)于函數(shù)SKIPIF1<0，把滿足SKIPIF1<0的實(shí)數(shù)SKIPIF1<0叫做函數(shù)SKIPIF1<0的不動(dòng)點(diǎn).設(shè)SKIPIF1<0，若SKIPIF1<0有兩個(gè)不動(dòng)點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．已知函數(shù)SKIPIF1<0，SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，不等式SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題15．對(duì)于函數(shù)SKIPIF1<0，下列說法正確的是（）A．SKIPIF1<0在SKIPIF1<0處取得極大值SKIPIF1<0 B．SKIPIF1<0有兩個(gè)不同的零點(diǎn)C．SKIPIF1<0 D．若SKIPIF1<0在SKIPIF1<0上恒成立，則SKIPIF1<016．關(guān)于函數(shù)SKIPIF1<0，SKIPIF1<0下列說法正確的是（）A．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0處的切線方程為SKIPIF1<0B．若函數(shù)SKIPIF1<0在SKIPIF1<0上恰有一個(gè)極值，則SKIPIF1<0C．對(duì)任意SKIPIF1<0，SKIPIF1<0恒成立D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上恰有2個(gè)零點(diǎn)三、解答題17．已知函數(shù)SKIPIF1<0，且SKIPIF1<0恒成立．（1）求實(shí)數(shù)SKIPIF1<0的值；（2）記SKIPIF1<0，若SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，不等式SKIPIF1<0恒成立，求SKIPIF1<0的最大值．18．已知函數(shù)SKIPIF1<0的圖象過點(diǎn)SKIPIF1<0，且在P處的切線恰好與直線SKIPIF1<0垂直．（1）求SKIPIF1<0的解析式；（2）若SKIPIF1<0在SKIPIF1<0上是減函數(shù)，求m的取值范圍．19．已知函數(shù)SKIPIF1<0（SKIPIF1<0）.（1）討論函數(shù)SKIPIF1<0的單調(diào)性；（2）若關(guān)于SKIPIF1<0的不等式SKIPIF1<0在SKIPIF1<0上恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍.20．已知函數(shù)SKIPIF1<0，SKIPIF1<0.（1）若曲線SKIPIF1<0在SKIPIF1<0處的切線與直線SKIPIF1<0垂直，求實(shí)數(shù)SKIPIF1<0的值；（2）設(shè)SKIPIF1<0，若對(duì)任意兩個(gè)不等的正數(shù)SKIPIF1<0，SKIPIF1<0，都有SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍；（3）若SKIPIF1<0上存在一點(diǎn)SKIPIF1<0，使得SKIPIF1<0成立，求實(shí)數(shù)SKIPIF1<0的取值范圍.21．已知函數(shù)SKIPIF1<0，SKIPIF1<0．（1）求函數(shù)SKIPIF1<0在SKIPIF1<0處的切線方程；（2）若實(shí)數(shù)SKIPIF1<0為整數(shù)，且對(duì)任意的SKIPIF1<0時(shí)，都有SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的最小值．22．設(shè)函數(shù)SKIPIF1<0.（1）求函數(shù)的單調(diào)區(qū)間；（2）若對(duì)于任意的SKIPIF1<0，不等式SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍.23．已知函數(shù)SKIPIF1<0的圖象在點(diǎn)SKIPIF1<0處的切線方程為SKIPIF1<0.(本題可能用的數(shù)據(jù)：SKIPIF1<0，SKIPIF1<0是自然對(duì)數(shù)的底數(shù))（1）求函數(shù)SKIPIF1<0的解析式；（2）若對(duì)任意SKIPIF1<0，不等式SKIPIF1<0恒成立，求整數(shù)t的最大值.24．已知函數(shù)SKIPIF1<0．（1）當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0