新高考數(shù)學(xué)一輪復(fù)習(xí) 導(dǎo)數(shù)專項(xiàng)重點(diǎn)難點(diǎn)突破專題07 函數(shù)單調(diào)性、極值、最值綜合運(yùn)用(原卷版)

專題07函數(shù)單調(diào)性、極值、最值綜合運(yùn)用一、單選題1．設(shè)函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0無最小值，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．已知函數(shù)SKIPIF1<0，則（

）A．函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增B．函數(shù)SKIPIF1<0在SKIPIF1<0上有兩個零點(diǎn)C．函數(shù)SKIPIF1<0有極大值16D．函數(shù)SKIPIF1<0有最小值SKIPIF1<03．如圖是函數(shù)SKIPIF1<0的導(dǎo)函數(shù)的圖象，下列結(jié)論中正確的是（

）A．SKIPIF1<0在SKIPIF1<0上是增函數(shù) B．當(dāng)SKIPIF1<0時，SKIPIF1<0取得最小值C．當(dāng)SKIPIF1<0時，SKIPIF1<0取得極大值 D．SKIPIF1<0在SKIPIF1<0上是增函數(shù)，在SKIPIF1<0上是減函數(shù)4．已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0在SKIPIF1<0上存在最小值，則a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．函數(shù)SKIPIF1<0有極小值，且極小值為0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．SKIPIF1<07．已知函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)存在最小值，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．若關(guān)于SKIPIF1<0的不等式SKIPIF1<0有且只有兩個整數(shù)解，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．已知函數(shù)SKIPIF1<0，若SKIPIF1<0是SKIPIF1<0在SKIPIF1<0上唯一的極值點(diǎn)，則實(shí)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，若SKIPIF1<0恒成立，則實(shí)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，則下列結(jié)論正確的是（

）A．函數(shù)SKIPIF1<0存在三個不同的零點(diǎn)B．函數(shù)SKIPIF1<0既存在極大值又存在極小值C．若SKIPIF1<0時，SKIPIF1<0，則t的最小值為2D．當(dāng)SKIPIF1<0時，方程SKIPIF1<0有且只有兩個實(shí)根12．函數(shù)SKIPIF1<0，其圖象在坐標(biāo)原點(diǎn)處與SKIPIF1<0相切，則（

）A．SKIPIF1<0B．函數(shù)SKIPIF1<0沒有最小值C．函數(shù)SKIPIF1<0存在兩個極值D．函數(shù)SKIPIF1<0存在兩個零點(diǎn)13．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14．已知函數(shù)SKIPIF1<0，則下列選項(xiàng)正確的有（

）A．函數(shù)SKIPIF1<0極小值為SKIPIF1<0，極大值為SKIPIF1<0.B．函數(shù)SKIPIF1<0存在3個不同的零點(diǎn).C．當(dāng)SKIPIF1<0時，函數(shù)SKIPIF1<0的最大值為SKIPIF1<0.D．當(dāng)SKIPIF1<0時，方程SKIPIF1<0恰有3個不等實(shí)根.15．對于函數(shù)SKIPIF1<0，下列選項(xiàng)正確的是（

）A．函數(shù)SKIPIF1<0極小值為SKIPIF1<0，極大值為SKIPIF1<0B．函數(shù)SKIPIF1<0單調(diào)遞減區(qū)間為SKIPIF1<0，單調(diào)遞增區(qū)為SKIPIF1<0C．函數(shù)SKIPIF1<0最小值為為SKIPIF1<0，最大值SKIPIF1<0D．函數(shù)SKIPIF1<0存在兩個零點(diǎn)1和SKIPIF1<016．已知SKIPIF1<0，SKIPIF1<0，則下列結(jié)論正確的是（

）A．函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值為3 B．SKIPIF1<0C．函數(shù)SKIPIF1<0的極值點(diǎn)有2個 D．函數(shù)SKIPIF1<0存在唯一零點(diǎn)SKIPIF1<017．已知函數(shù)SKIPIF1<0，則下列說法正確的是（

）A．若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0在SKIPIF1<0單調(diào)遞減B．若SKIPIF1<0，則SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0有最小值D．若SKIPIF1<0有解，則實(shí)數(shù)c的最小值為－1三、填空題18．若函SKIPIF1<0只有一個極值點(diǎn)，則k的取值范圍為______．19．已知函數(shù)SKIPIF1<0，若對任意SKIPIF1<0恒成立，則m的最大值為___________.四、解答題20．已知函數(shù)SKIPIF1<0，SKIPIF1<0是SKIPIF1<0的一個極值點(diǎn)．(1)求實(shí)數(shù)a的值；(2)求SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值和最小值．21．已知函數(shù)SKIPIF1<0，SKIPIF1<0.（1）求SKIPIF1<0的單調(diào)區(qū)間；（2）若SKIPIF1<0，且SKIPIF1<0的極小值小于SKIPIF1<0，求a的取值范圍.22．已知SKIPIF1<0，SKIPIF1<0．（Ⅰ）討論SKIPIF1<0的單調(diào)性；（Ⅱ）若SKIPIF1<0，證明：SKIPIF1<0．23．已知函數(shù)SKIPIF1<0．（1）當(dāng)SKIPIF1<0時,求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；（2）若函數(shù)SKIPIF1<0在SKIPIF1<0處取得極值,求函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值與最小值．24．已知函數(shù)SKIPIF1<0，曲線SKIPIF1<0在SKIPIF1<0處的切線方程為SKIPIF1<0SKIPIF1<0求SKIPIF1<0的值；SKIPIF1<0若函數(shù)SKIPIF1<0存在極大值，求SKIPIF1<0的取值范圍.25．已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0是SKIPIF1<0的極小值點(diǎn)，求SKIPIF1<0的值；(2)若SKIPIF1<0，且SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，求SKIPIF1<0的取值范圍．26．已知SKIPIF1<0，函數(shù)SKIPIF1<0.(1)討論SKIPIF1<0的單調(diào)性；(2)當(dāng)SKIPIF1<0時，若對SKIPIF1<0恒成立,求實(shí)數(shù)b的最大值.27．已知SKIPIF1<0.（1）若函數(shù)SKIPIF1<0在SKIPIF1<0處取得極值，求實(shí)數(shù)SKIPIF1<0的值；（2）若SKIPIF1<0，求函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間；（3）若SKIPIF1<0，存在正實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0成立，求SKIPIF1<0