新高考數(shù)學(xué)二輪復(fù)習(xí)重難點(diǎn)突破專題22 導(dǎo)數(shù)解決函數(shù)零點(diǎn)交點(diǎn)和方程根的問題(原卷版)

專題22導(dǎo)數(shù)解決函數(shù)零點(diǎn)交點(diǎn)和方程根的問題一、單選題1．已知關(guān)于SKIPIF1<0的方程SKIPIF1<0有三個(gè)不等的實(shí)數(shù)根，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)3．已知函數(shù)SKIPIF1<0（SKIPIF1<0）與SKIPIF1<0（SKIPIF1<0）的圖象有且僅有兩個(gè)公共點(diǎn)，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．已知函數(shù)SKIPIF1<0，則下列說法正確的是（）A．存在SKIPIF1<0、SKIPIF1<0，函數(shù)SKIPIF1<0沒有零點(diǎn)B．任意SKIPIF1<0，存在SKIPIF1<0，函數(shù)SKIPIF1<0恰有SKIPIF1<0個(gè)零點(diǎn)C．任意SKIPIF1<0，存在SKIPIF1<0，函數(shù)SKIPIF1<0恰有SKIPIF1<0個(gè)零點(diǎn)D．任意SKIPIF1<0，存在SKIPIF1<0，函數(shù)SKIPIF1<0恰有SKIPIF1<0個(gè)零點(diǎn)5．函數(shù)SKIPIF1<0有且只有一個(gè)零點(diǎn)，則SKIPIF1<0的值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．SKIPIF1<06．已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0的圖象有且僅有三個(gè)交點(diǎn)，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0） B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0有兩個(gè)不同的零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．已知函數(shù)SKIPIF1<0有兩個(gè)零點(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<09．已知函數(shù)SKIPIF1<0，若恰有3個(gè)互不相同的實(shí)數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0，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或SKIPIF1<010．已知函數(shù)SKIPIF1<0恰有三個(gè)零點(diǎn)，則（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知函數(shù)SKIPIF1<0有兩個(gè)零點(diǎn)，則SKIPIF1<0的取值范圍（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．若函數(shù)SKIPIF1<0恰有兩個(gè)不同的零點(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<0二、多選題13．函數(shù)SKIPIF1<0在SKIPIF1<0上有唯一零點(diǎn)SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<014．已知函數(shù)SKIPIF1<0，給出下列四個(gè)結(jié)論，其中正確的是（）A．曲線SKIPIF1<0在SKIPIF1<0處的切線方程為SKIPIF1<0B．SKIPIF1<0恰有2個(gè)零點(diǎn)C．SKIPIF1<0既有最大值，又有最小值D．若SKIPIF1<0且SKIPIF1<0，則SKIPIF1<015．已知函數(shù)SKIPIF1<0，則下列說法正確的有（）A．直線y=0為曲線y=f(x)的一條切線B．f(x)的極值點(diǎn)個(gè)數(shù)為3C．f(x)的零點(diǎn)個(gè)數(shù)為4D．若f(SKIPIF1<0)=f(SKIPIF1<0)(SKIPIF1<0≠SKIPIF1<0)，則SKIPIF1<0+SKIPIF1<0=016．已知函數(shù)SKIPIF1<0有兩個(gè)零點(diǎn)SKIPIF1<0、SKIPIF1<0，且SKIPIF1<0，則下列結(jié)論不正確的是（）A．SKIPIF1<0 B．SKIPIF1<0的值隨SKIPIF1<0的增大而減小C．SKIPIF1<0 D．SKIPIF1<0三、解答題17．已知函數(shù)SKIPIF1<0，SKIPIF1<0．（1）討論函數(shù)SKIPIF1<0在SKIPIF1<0上的單調(diào)性；（2）求函數(shù)SKIPIF1<0在SKIPIF1<0上的零點(diǎn)個(gè)數(shù)．18．已知函數(shù)SKIPIF1<0．（1）當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；（2）若函數(shù)SKIPIF1<0只有1個(gè)零點(diǎn)，求實(shí)數(shù)SKIPIF1<0的取值范圍．19．已知函數(shù)SKIPIF1<0，SKIPIF1<0．（1）求SKIPIF1<0的最值；（2）若SKIPIF1<0，求關(guān)于SKIPIF1<0的方程SKIPIF1<0（SKIPIF1<0）的實(shí)數(shù)根的個(gè)數(shù)．20．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．21．設(shè)函數(shù)SKIPIF1<0．（1）當(dāng)SKIPIF1<0時(shí)，討論SKIPIF1<0在SKIPIF1<0內(nèi)的單調(diào)性；（2）當(dāng)SKIPIF1<0時(shí)，證明：SKIPIF1<0有且僅有兩個(gè)零點(diǎn)．22．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.23．已知函數(shù)SKIPIF1<0，a為非零常數(shù).（1）求SKIPIF1<0單調(diào)遞減區(qū)間；（2）討論方程SKIPIF1<0的根的個(gè)數(shù).24．已知函數(shù)SKIPIF1<0，SKIPIF1<0．（1）求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；（2）若關(guān)于SKIPIF1<0的方程SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)無零點(diǎn)，求實(shí)數(shù)SKIPIF1<0的取值范圍．25．設(shè)SKIPIF1<0為實(shí)數(shù)，已知函數(shù)SKIPIF1<0.（1）當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的單調(diào)區(qū)間；（2）當(dāng)SKIPIF1<0時(shí)，若SKIPIF1<0有兩個(gè)不同的零點(diǎn)，求SKIPIF1<0的取值范圍.26．設(shè)函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的取值范圍；(2)已知函數(shù)SKIPIF1<0存在兩個(gè)不同零點(diǎn)SKIPIF1<0，SKIPIF1<0，求滿足條件的最小正整數(shù)SKIPIF1<0的值.27．若函數(shù)SKIPIF1<0在SKIPIF1<0時(shí)，函數(shù)值SKIPIF1<0的取值區(qū)間恰為SKIPIF1<0，則稱SKIPIF1<0為SKIPIF1<0的一個(gè)“SKIPIF1<0倍倒域區(qū)間”.定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)SKIPIF1<0.（1）求SKIPIF1<0的解析式；（2）求SKIPIF1<0在SKIPIF1<0