新高考數(shù)學一輪復習 導數(shù)專項重點難點突破專題17 參變分離法解決導數(shù)問題(原卷版)

專題17參變分離法解決導數(shù)問題1.分離變量法在處理含參SKIPIF1<0的函數(shù)SKIPIF1<0不等式和方程問題時，有時可以將變量分離出來，如將方程SKIPIF1<0，轉(zhuǎn)化為SKIPIF1<0這樣就將把研究含參函數(shù)SKIPIF1<0與SKIPIF1<0軸的位置關(guān)系的問題轉(zhuǎn)化為不含參的函數(shù)SKIPIF1<0與動直線SKIPIF1<0的位置關(guān)系問題，這種處理方法就叫分離變量法。（1）優(yōu)點：分離變量法可以將含參函數(shù)中的參數(shù)分離出去，避免直接討論，從而簡化運算；（2）解題過程中可能遇到的問題：①參數(shù)無法分離；②參數(shù)分離后的函數(shù)SKIPIF1<0過于復雜；③討論位置關(guān)系時可能用到SKIPIF1<0的函數(shù)極限，造成說理困難.2.分類：分離參數(shù)法有完全分離參數(shù)法（全分參）和部分分離參數(shù)法（半分參）兩種注意事項：無論哪種分參方法，分參過程中需注意變量的正負對不等號的影響！一、單選題1．已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．若函數(shù)SKIPIF1<0在SKIPIF1<0上是增函數(shù)，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知函數(shù)SKIPIF1<0（SKIPIF1<0為自然對數(shù)的底數(shù)），若SKIPIF1<0在SKIPIF1<0上恒成立，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．關(guān)于x的方程SKIPIF1<0在SKIPIF1<0內(nèi)有解，則實數(shù)m的取值范圍（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．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<06．若對任意正實數(shù)x，不等式SKIPIF1<0恒成立，則實數(shù)a的范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知函數(shù)SKIPIF1<0，若存在SKIPIF1<0，使得SKIPIF1<0，則實數(shù)a的取值范圍為：（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．當SKIPIF1<0時，SKIPIF1<0恒成立，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．對任意SKIPIF1<0，不等式SKIPIF1<0恒成立，則正數(shù)a的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．e10．已知函數(shù)SKIPIF1<0，若當SKIPIF1<0時，SKIPIF1<0有解，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11．已知函數(shù)SKIPIF1<0有兩個零點SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則下列選項正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0在SKIPIF1<0上單調(diào)遞增C．SKIPIF1<0 D．若SKIPIF1<0，則SKIPIF1<012．已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上只有一個零點，則實數(shù)SKIPIF1<0可取的值有（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．設(shè)函數(shù)SKIPIF1<0(e為自然對數(shù)的底數(shù)).若存在SKIPIF1<0使SKIPIF1<0成立，則實數(shù)a的取值可以是（

）A．0 B．1 C．2 D．314．已知定義在R上的奇函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則“對于任意的SKIPIF1<0，不等式SKIPIF1<0恒成立”的充分不必要條件可以是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、填空題15．若函數(shù)SKIPIF1<0是R上的減函數(shù)，則實數(shù)a的最小值為_______16．已知函數(shù)SKIPIF1<0，若對任意正數(shù)SKIPIF1<0，當SKIPIF1<0時，都有SKIPIF1<0成立，則實數(shù)m的取值范圍是______．17．已知函數(shù)SKIPIF1<0，若對任意的SKIPIF1<0，不等式SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的取值范圍為___________.18．已知SKIPIF1<0，若關(guān)于SKIPIF1<0的不等式SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的取值范圍是________．四、解答題19．已知函數(shù)SKIPIF1<0.（1）求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值和最小值(參考數(shù)據(jù)：SKIPIF1<0)；（2）若不等式SKIPIF1<0有解，求實數(shù)a的取值范圍.20．已知函數(shù)SKIPIF1<0，SKIPIF1<0.（1）若SKIPIF1<0的圖像在SKIPIF1<0處的切線經(jīng)過點SKIPIF1<0，求SKIPIF1<0的值；（2）當SKIPIF1<0時，不等式SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍.21．已知函數(shù)SKIPIF1<0，曲線SKIPIF1<0在點SKIPIF1<0處的切線SKIPIF1<0的斜率為4.(1)求切線SKIPIF1<0的方程；(2)若關(guān)于SKIPIF1<0的不等式SKIPIF1<0恒成立，求實數(shù)SKIPIF1<0的取值范圍.22．已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0，不等式SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍；(2)若曲線SKIPIF1<0存在過點SKIPIF1<0的切線，求證：SKIPIF1<0．23．已知函數(shù)SKIPIF1<0(1)當SKIPIF1<0時，求函數(shù)f（x）的單調(diào)區(qū)間；(2)若函數(shù)SKIPIF1<0在SKIPIF1<0上有兩個極值點，求實數(shù)SKIPIF1<0的取值范圍.24．已知函數(shù)SKIPIF1<0的圖象在點SKIPIF1<0處的切線與直線SKIPIF1<0平行（e是自然對數(shù)的底數(shù)）.(1)求函數(shù)SKIPIF1<0的解析式；(2)若SKIPIF1<0在SKIPIF1<0上恒成立，求實數(shù)k的取值范圍.25．已知函數(shù)SKIPIF1<0.(1)當SKIPIF1<0時，求SKIPIF1<0的單調(diào)區(qū)間；(2)當SKIPIF1<0時，SKIPIF1<0，求SKIPIF1<0的取值范圍.26．已知函數(shù)SKIPIF1<0，SKIPIF1<0.（1）若SKIPIF1<0在SKIPIF1<0處取得極值，求SKIPIF1<0的值；（2）若SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，求SKIPIF1<0的取值范圍；（3）若函數(shù)SKIPIF1<0有一個零點，求SKIPIF1<0的取值范圍.27．已知函數(shù)SKIPIF1<0.（I）求函數(shù)SKIPIF1<0的單調(diào)區(qū)間和極值；（II）若不等式SKIPIF1<0在區(qū)間SKIPIF1<0上恒成立，求實數(shù)SKIPIF1<0的取值范圍.28．已知函數(shù)SKIPIF1<0．(1)求函數(shù)SKIPIF1<0