新高考數(shù)學(xué)二輪復(fù)習(xí)重難點(diǎn)突破專題20 利用導(dǎo)數(shù)解決函數(shù)的極值點(diǎn)問題(原卷版)

專題20利用導(dǎo)數(shù)解決函數(shù)的極值點(diǎn)問題一、單選題1．已知函數(shù)SKIPIF1<0，則下列結(jié)論錯(cuò)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(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0恰有三個(gè)零點(diǎn)D．當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0恰有兩個(gè)極值點(diǎn)2．如圖是函數(shù)SKIPIF1<0的導(dǎo)函數(shù)SKIPIF1<0的圖象，則函數(shù)SKIPIF1<0的極小值點(diǎn)的個(gè)數(shù)為（）A．0 B．1 C．2 D．33．已知函數(shù)SKIPIF1<0的導(dǎo)函數(shù)SKIPIF1<0，若SKIPIF1<0在SKIPIF1<0處取得極大值，則實(shí)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(wú)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<05．已知函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)，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(shí)滿足條件：①SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的一個(gè)極大值點(diǎn)；②SKIPIF1<0，SKIPIF1<0.則實(shí)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(gè)不同的極值點(diǎn)，則實(shí)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(shè)函數(shù)SKIPIF1<0，則下列是函數(shù)SKIPIF1<0極小值點(diǎn)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(gè)極值點(diǎn)是SKIPIF1<0和SKIPIF1<0，則點(diǎn)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(diǎn)，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(diǎn)為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．若函數(shù)SKIPIF1<0有兩個(gè)不同的極值點(diǎn)，則實(shí)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(shè)函數(shù)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0是SKIPIF1<0的極值點(diǎn)C．SKIPIF1<0存在零點(diǎn) 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(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0處的切線方程為SKIPIF1<0B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0存在惟一極小值點(diǎn)SKIPIF1<0C．對(duì)任意SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上均存在零點(diǎn)D．存在SKIPIF1<0，SKIPIF1<0在SKIPIF1<0有且只有一個(gè)零點(diǎn)18．已知函數(shù)SKIPIF1<0，SKIPIF1<0，則下列說(shuō)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(gè)極值點(diǎn)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(diǎn)個(gè)數(shù)為4 B．SKIPIF1<0的極值點(diǎn)個(gè)數(shù)為3C．x軸為曲線SKIPIF1<0的切線 D．若SKIPIF1<0，則SKIPIF1<020．設(shè)函數(shù)SKIPIF1<0，則下列說(shuō)法正確的是（）A．SKIPIF1<0定義域是SKIPIF1<0 B．SKIPIF1<0時(shí)，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(gè)極值點(diǎn)三、解答題21．已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0只有一個(gè)極值點(diǎn)，求SKIPIF1<0的取值范圍.(2)若函數(shù)SKIPIF1<0存在兩個(gè)極值點(diǎn)SKIPIF1<0，記過點(diǎn)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(gè)零點(diǎn)，求SKIPIF1<0的取值范圍；（2）若SKIPIF1<0在SKIPIF1<0處有極大值SKIPIF1<0，求當(dāng)SKIPIF1<0時(shí)SKIPIF1<0的值域．23．（1）當(dāng)SKIPIF1<0時(shí)，求證：SKIPIF1<0；（2）若SKIPIF1<0對(duì)于任意的SKIPIF1<0恒成立，求實(shí)數(shù)k的取值范圍；（3）設(shè)a>0，求證；函數(shù)SKIPIF1<0在SKIPIF1<0上存在唯一的極大值點(diǎn)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(shè)SKIPIF1<0是函數(shù)SKIPIF1<0的兩個(gè)極值點(diǎn)，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(gè)極值點(diǎn)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(duì)應(yīng)的極值點(diǎn)．（2）若函數(shù)SKIPIF1<0，且SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，求實(shí)數(shù)SKIPIF1<0的取值范圍．27．已知函數(shù)SKIPIF1<0，其導(dǎo)函數(shù)為SKIPIF1<0，且SKIPIF1<0.（1）求a的值；（2）設(shè)函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)SKIPIF1<0，SKIPIF1<0，求b的取值范圍，并證明過兩點(diǎn)SKIPIF1<0，SKIPIF1<0的直線m恒過定點(diǎn)，且求出該定點(diǎn)坐標(biāo)SKIPIF1<0（3）當(dāng)SKIPIF1<0時(shí)，證明函數(shù)SKIPIF1<0在R上只有一個(gè)零點(diǎn).28．設(shè)函數(shù)SKIPIF1<0，其中SKIPIF1<0.（1）若曲線SKIPIF1<0