新高考數(shù)學二輪復習重難點突破專題25 參變分離法解決導數(shù)問題(原卷版)

專題25參變分離法解決導數(shù)問題一、單選題1．已知函數(shù)SKIPIF1<0SKIPIF1<0，且SKIPIF1<0，當SKIPIF1<0時，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，則實數(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為自然對數(shù)的底數(shù)），SKIPIF1<0．若存在實數(shù)SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0，且SKIPIF1<0，則實數(shù)SKIPIF1<0的最大值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．15．設函數(shù)SKIPIF1<0在SKIPIF1<0上有兩個零點，則實數(shù)a的取值范圍（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知關于x的方程SKIPIF1<0在SKIPIF1<0上有兩解，則實數(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上單調遞增，則實數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．若關于x的不等式（a+2）x≤x2+alnx在區(qū)間[SKIPIF1<0，e]（e為自然對數(shù)的底數(shù)）上有實數(shù)解，則實數(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為自然對數(shù)的底數(shù)）.若存在SKIPIF1<0，使得SKIPIF1<0，則實數(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有兩個極值點，則實數(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上單調遞減，則實數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<013．對于函數(shù)SKIPIF1<0，把滿足SKIPIF1<0的實數(shù)SKIPIF1<0叫做函數(shù)SKIPIF1<0的不動點.設SKIPIF1<0，若SKIPIF1<0有兩個不動點，則實數(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SKIPIF1<0時，不等式SKIPIF1<0恒成立，則實數(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有兩個不同的零點C．SKIPIF1<0 D．若SKIPIF1<0在SKIPIF1<0上恒成立，則SKIPIF1<016．關于函數(shù)SKIPIF1<0，SKIPIF1<0下列說法正確的是（）A．當SKIPIF1<0時，SKIPIF1<0在SKIPIF1<0處的切線方程為SKIPIF1<0B．若函數(shù)SKIPIF1<0在SKIPIF1<0上恰有一個極值，則SKIPIF1<0C．對任意SKIPIF1<0，SKIPIF1<0恒成立D．當SKIPIF1<0時，SKIPIF1<0在SKIPIF1<0上恰有2個零點三、解答題17．已知函數(shù)SKIPIF1<0，且SKIPIF1<0恒成立．（1）求實數(shù)SKIPIF1<0的值；（2）記SKIPIF1<0，若SKIPIF1<0，且當SKIPIF1<0時，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的單調性；（2）若關于SKIPIF1<0的不等式SKIPIF1<0在SKIPIF1<0上恒成立，求實數(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，求實數(shù)SKIPIF1<0的值；（2）設SKIPIF1<0，若對任意兩個不等的正數(shù)SKIPIF1<0，SKIPIF1<0，都有SKIPIF1<0恒成立，求實數(shù)SKIPIF1<0的取值范圍；（3）若SKIPIF1<0上存在一點SKIPIF1<0，使得SKIPIF1<0成立，求實數(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）若實數(shù)SKIPIF1<0為整數(shù)，且對任意的SKIPIF1<0時，都有SKIPIF1<0恒成立，求實數(shù)SKIPIF1<0的最小值．22．設函數(shù)SKIPIF1<0.（1）求函數(shù)的單調區(qū)間；（2）若對于任意的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SKIPIF1<0處的切線方程為SKIPIF1<0.(本題可能用的數(shù)據：SKIPIF1<0，SKIPIF1<0是自然對數(shù)的底數(shù))（1）求函數(shù)SKIPIF1<0的解析式；（2）若對任意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SKIPIF1<0時，求SKIPIF1<0