專題20利用導數(shù)解決函數(shù)的極值點問題一、單選題1．已知函數(shù)SKIPIF1<0，則下列結(jié)論錯誤的是（）A．SKIPIF1<0是奇函數(shù)B．若SKIPIF1<0，則SKIPIF1<0是增函數(shù)C．當SKIPIF1<0時，函數(shù)SKIPIF1<0恰有三個零點D．當SKIPIF1<0時，函數(shù)SKIPIF1<0恰有兩個極值點2．如圖是函數(shù)SKIPIF1<0的導函數(shù)SKIPIF1<0的圖象，則函數(shù)SKIPIF1<0的極小值點的個數(shù)為（）A．0 B．1 C．2 D．33．已知函數(shù)SKIPIF1<0的導函數(shù)SKIPIF1<0，若SKIPIF1<0在SKIPIF1<0處取得極大值，則實數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．若函數(shù)SKIPIF1<0無極值點則實數(shù)a的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知函數(shù)SKIPIF1<0有兩個極值點，則a的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．“SKIPIF1<0”是“函數(shù)SKIPIF1<0在SKIPIF1<0上有極值”的（）A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分也不必要條件7．已知函數(shù)SKIPIF1<0，若同時滿足條件：①SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的一個極大值點；②SKIPIF1<0，SKIPIF1<0.則實數(shù)a的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．若函數(shù)SKIPIF1<0（SKIPIF1<0為常數(shù)）有兩個不同的極值點，則實數(shù)SKIPIF1<0取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．已知函數(shù)SKIPIF1<0在SKIPIF1<0處取得極值，則SKIPIF1<0（）A．1 B．2 C．SKIPIF1<0 D．-210．設函數(shù)SKIPIF1<0，則下列是函數(shù)SKIPIF1<0極小值點的是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．函數(shù)SKIPIF1<0的圖象大致是()A． B．C． D．12．已函數(shù)SKIPIF1<0的兩個極值點是SKIPIF1<0和SKIPIF1<0，則點SKIPIF1<0的軌跡是（）A．橢圓弧 B．圓弧 C．雙曲線弧 D．拋物線弧13．若SKIPIF1<0是函數(shù)SKIPIF1<0的極值點，則SKIPIF1<0的值是（）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．已知函數(shù)SKIPIF1<0，則SKIPIF1<0）的極大值點為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．若函數(shù)SKIPIF1<0有兩個不同的極值點，則實數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題16．設函數(shù)SKIPIF1<0的導函數(shù)為SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0是SKIPIF1<0的極值點C．SKIPIF1<0存在零點 D．SKIPIF1<0在SKIPIF1<0單調(diào)遞增17．關(guān)于函數(shù)SKIPIF1<0，SKIPIF1<0，下列結(jié)論正確的有（）A．當SKIPIF1<0時，SKIPIF1<0在SKIPIF1<0處的切線方程為SKIPIF1<0B．當SKIPIF1<0時，SKIPIF1<0存在惟一極小值點SKIPIF1<0C．對任意SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上均存在零點D．存在SKIPIF1<0，SKIPIF1<0在SKIPIF1<0有且只有一個零點18．已知函數(shù)SKIPIF1<0，SKIPIF1<0，則下列說法正確的有（）A．SKIPIF1<0是偶函數(shù)B．SKIPIF1<0是周期函數(shù)C．在區(qū)間SKIPIF1<0上，SKIPIF1<0有且只有一個極值點D．過(0，0)作SKIPIF1<0的切線，有且僅有3條19．已知SKIPIF1<0.（）A．SKIPIF1<0的零點個數(shù)為4 B．SKIPIF1<0的極值點個數(shù)為3C．x軸為曲線SKIPIF1<0的切線 D．若SKIPIF1<0，則SKIPIF1<020．設函數(shù)SKIPIF1<0，則下列說法正確的是（）A．SKIPIF1<0定義域是SKIPIF1<0 B．SKIPIF1<0時，SKIPIF1<0圖象位于SKIPIF1<0軸下方C．SKIPIF1<0存在單調(diào)遞增區(qū)間 D．SKIPIF1<0有且僅有一個極值點三、解答題21．已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0只有一個極值點，求SKIPIF1<0的取值范圍.(2)若函數(shù)SKIPIF1<0存在兩個極值點SKIPIF1<0，記過點SKIPIF1<0的直線的斜率為SKIPIF1<0，證明：SKIPIF1<0.22．已知函數(shù)SKIPIF1<0．（1）若SKIPIF1<0是奇函數(shù)，且有三個零點，求SKIPIF1<0的取值范圍；（2）若SKIPIF1<0在SKIPIF1<0處有極大值SKIPIF1<0，求當SKIPIF1<0時SKIPIF1<0的值域．23．（1）當SKIPIF1<0時，求證：SKIPIF1<0；（2）若SKIPIF1<0對于任意的SKIPIF1<0恒成立，求實數(shù)k的取值范圍；（3）設a>0，求證；函數(shù)SKIPIF1<0在SKIPIF1<0上存在唯一的極大值點SKIPIF1<0，且SKIPIF1<0.24．已知函數(shù)SKIPIF1<0.（1）討論函數(shù)SKIPIF1<0的單調(diào)性.（2）若SKIPIF1<0，設SKIPIF1<0是函數(shù)SKIPIF1<0的兩個極值點，若SKIPIF1<0，求證:SKIPIF1<0.25．已知函數(shù)SKIPIF1<0（1）討論SKIPIF1<0的單調(diào)性；（2）若SKIPIF1<0有兩個極值點SKIPIF1<0，求SKIPIF1<0的取值范圍.26．已知函數(shù)SKIPIF1<0SKIPIF1<0，SKIPIF1<0是偶函數(shù)．（1）求函數(shù)SKIPIF1<0的極值以及對應的極值點．（2）若函數(shù)SKIPIF1<0，且SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，求實數(shù)SKIPIF1<0的取值范圍．27．已知函數(shù)SKIPIF1<0，其導函數(shù)為SKIPIF1<0，且SKIPIF1<0.（1）求a的值；（2）設函數(shù)SKIPIF1<0有兩個極值點SKIPIF1<0，SKIPIF1<0，求b的取值范圍，并證明過兩點SKIPIF1<0，SKIPIF1<0的直線m恒過定點，且求出該定點坐標SKIPIF1<0（3）當SKIPIF1<0時，證明函數(shù)SKIPIF1<0在R上只有一個零點.28．設函數(shù)SKIPIF1<0，其中SKIPIF1<0.（1）若曲線SKIPIF1<0