新高考數(shù)學(xué)二輪復(fù)習(xí)重難點(diǎn)突破專(zhuān)題18 利用函數(shù)的極值求參數(shù)值(原卷版)

專(zhuān)題18利用函數(shù)的極值求參數(shù)值一、單選題1．若函數(shù)SKIPIF1<0的極值為SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0是函數(shù)SKIPIF1<0的極小值點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0且SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0且SKIPIF1<0 D．SKIPIF1<03．若SKIPIF1<0，SKIPIF1<0，且函數(shù)SKIPIF1<0在SKIPIF1<0處有極值，則SKIPIF1<0的最大值等于（）.A．16 B．25 C．36 D．494．若函數(shù)SKIPIF1<0不存在極值點(diǎn)，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．函數(shù)SKIPIF1<0在SKIPIF1<0處取得極值，則（）A．SKIPIF1<0，且SKIPIF1<0為極大值點(diǎn) B．SKIPIF1<0，且SKIPIF1<0為極小值點(diǎn)C．SKIPIF1<0，且SKIPIF1<0為極大值點(diǎn) D．SKIPIF1<0，且SKIPIF1<0為極小值點(diǎn)6．已知SKIPIF1<0在SKIPIF1<0處取得極值，則SKIPIF1<0的最小值是（）A．SKIPIF1<0 B．2 C．SKIPIF1<0 D．SKIPIF1<07．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)有極小值，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知函數(shù)SKIPIF1<0的極大值為4，若函數(shù)SKIPIF1<0在SKIPIF1<0上的極小值不大于SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．已知函數(shù)SKIPIF1<0在SKIPIF1<0處取極大值，則SKIPIF1<0（）A．－2或－6 B．2或6 C．6 D．210．已知a為常數(shù)，函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)x1，x2(x1＜x2)，則下列結(jié)論正確的是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、解答題11．已知函數(shù)SKIPIF1<0（SKIPIF1<0為自然對(duì)數(shù)的底數(shù)）.（1）當(dāng)SKIPIF1<0時(shí)，求證：函數(shù)SKIPIF1<0在SKIPIF1<0上恰有一個(gè)零點(diǎn)；（2）若函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)，求實(shí)數(shù)SKIPIF1<0的取值范圍.12．已知函數(shù)SKIPIF1<0，且SKIPIF1<0在SKIPIF1<0處取得極值．（Ⅰ）求b的值；（Ⅱ）若當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0恒成立，求c的取值范圍；（Ⅲ）對(duì)任意的SKIPIF1<0，SKIPIF1<0是否恒成立？如果成立，給出證明；如果不成立，請(qǐng)說(shuō)明理由．13．設(shè)函數(shù)SKIPIF1<0，其圖像與SKIPIF1<0軸交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且SKIPIF1<0．（I）求SKIPIF1<0的取值范圍；（Ⅱ）證明：SKIPIF1<0．14．已知函數(shù)SKIPIF1<0.（1）若SKIPIF1<0是函數(shù)SKIPIF1<0的一個(gè)極值點(diǎn)，求SKIPIF1<0的值；（2）當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍.15．已知函數(shù)SKIPIF1<0，SKIPIF1<0且SKIPIF1<0（1）若函數(shù)SKIPIF1<0在SKIPIF1<0處取得極值SKIPIF1<0，求函數(shù)SKIPIF1<0的解析式；（2）在（1）的條件下，令SKIPIF1<0，求SKIPIF1<0的單調(diào)區(qū)間；16．設(shè)函數(shù)SKIPIF1<0（1）若函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)，求SKIPIF1<0實(shí)數(shù)的取值范圍；（2）設(shè)SKIPIF1<0，若當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0的兩個(gè)極值點(diǎn)SKIPIF1<0，SKIPIF1<0滿(mǎn)足SKIPIF1<0，求證：SKIPIF1<0.17．已知函數(shù)SKIPIF1<0在SKIPIF1<0處取得極值．（1）求實(shí)數(shù)a的值．（2）當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0的最小值．18．設(shè)函數(shù)SKIPIF1<0．（1）若曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線與SKIPIF1<0軸平行，求SKIPIF1<0；（2）若SKIPIF1<0在SKIPIF1<0處取得極小值，求SKIPIF1<0的取值范圍．19．已知函數(shù)SKIPIF1<0.（1）當(dāng)SKIPIF1<0時(shí)，求證：SKIPIF1<0恰有1個(gè)零點(diǎn)；（2）若SKIPIF1<0存在極大值，且極大值小于0，求a的取值范圍.20．已知函數(shù)SKIPIF1<0，SKIPIF1<0是SKIPIF1<0的導(dǎo)函數(shù).（1）若SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)有唯一的極小值，求SKIPIF1<0的取值范圍；（2）若SKIPIF1<0，SKIPIF1<0，試研究SKIPIF1<0的零點(diǎn)個(gè)數(shù).21．設(shè)函數(shù)SKIPIF1<0，其中SKIPIF1<0.（Ⅰ）若SKIPIF1<0，求曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程；（Ⅱ）若函數(shù)SKIPIF1<0在SKIPIF1<0上有極大值，求SKIPIF1<0的取值范圍.22．已知函數(shù)SKIPIF1<0.（1）求函數(shù)SKIPIF1<0在SKIPIF1<0處的切線方程；（2）若不等式SKIPIF1<0對(duì)任意的SKIPIF1<0都成立，求實(shí)數(shù)m的取值范圍.23．已知函數(shù)SKIPIF1<0.(Ⅰ)求曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程；(Ⅱ)若函數(shù)SKIPIF1<0在SKIPIF1<0上有極值，求SKIPIF1<0的取值范圍．24．已知函數(shù)SKIPIF1<0.（Ⅰ）當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；（Ⅱ）若函數(shù)SKIPIF1<0在SKIPIF1<0處取得極大值，求實(shí)數(shù)m的取值范圍.25．已知函數(shù)SKIPIF1<0.（1）若SKIPIF1<0在SKIPIF1<0處取得極值，求SKIPIF1<0的值；（2）求函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值.26．已知函數(shù)SKIPIF1<0（SKIPIF1<0）.（1）若SKIPIF1<0是函數(shù)的極值點(diǎn)，求a的值及函數(shù)SKIPIF1<0的極值；（2）討論函數(shù)的單調(diào)性.27．已知函數(shù)SKIPIF1<0（1）若SKIPIF1<0，函數(shù)SKIPIF1<0的極大值為SKIPIF1<0，求a的值；（2）若對(duì)任意的SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍.28．已知函數(shù)SKIPIF1<0在SKIPIF1<0