新高考數(shù)學(xué)一輪復(fù)習(xí) 講與練第10講 導(dǎo)數(shù)與函數(shù)的單調(diào)性（原卷版）

第10講導(dǎo)數(shù)與函數(shù)的單調(diào)性學(xué)校____________姓名____________班級____________一、知識梳理1.函數(shù)的單調(diào)性與導(dǎo)數(shù)的關(guān)系條件恒有結(jié)論函數(shù)y＝f(x)在區(qū)間(a，b)上可導(dǎo)f′(x)＞0f(x)在(a，b)上單調(diào)遞增f′(x)＜0f(x)在(a，b)上單調(diào)遞減f′(x)＝0f(x)在(a，b)上是常數(shù)函數(shù)2.利用導(dǎo)數(shù)判斷函數(shù)單調(diào)性的步驟第1步，確定函數(shù)的定義域；第2步，求出導(dǎo)函數(shù)f′(x)的零點(diǎn)；第3步，用f′(x)的零點(diǎn)將f(x)的定義域劃分為若干個區(qū)間，列表給出f′(x)在各區(qū)間上的正負(fù)，由此得出函數(shù)y＝f(x)在定義域內(nèi)的單調(diào)性.考點(diǎn)和典型例題【典例1】不含參函數(shù)的單調(diào)性1．（2022·湖北·房縣第一中學(xué)模擬預(yù)測）已知函數(shù)SKIPIF1<0，不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2021·西藏·林芝市第二高級中學(xué)高三階段練習(xí)（理））函數(shù)SKIPIF1<0的單調(diào)增區(qū)間是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·河南·模擬預(yù)測（文））已知函數(shù)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，若對任意的SKIPIF1<0，都有SKIPIF1<0，且SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·浙江金華·模擬預(yù)測）已知函數(shù)SKIPIF1<0(1)當(dāng)SKIPIF1<0時，討論SKIPIF1<0的單調(diào)區(qū)間；(2)當(dāng)SKIPIF1<0時，若SKIPIF1<0有兩個零點(diǎn)SKIPIF1<0，且SKIPIF1<0，求證：SKIPIF1<0.5．（2022·河南·模擬預(yù)測（文））已知函數(shù)SKIPIF1<0，（SKIPIF1<0且SKIPIF1<0）.(1)當(dāng)SKIPIF1<0時，求SKIPIF1<0的單調(diào)區(qū)間；(2)若函數(shù)SKIPIF1<0有兩個零點(diǎn)，求a的取值范圍.【典例2】含參函數(shù)的單調(diào)性1．（2022·四川綿陽·二模（文））若SKIPIF1<0是函數(shù)SKIPIF1<0的極大值點(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<02．（2021·湖北·應(yīng)城市第一高級中學(xué)高三階段練習(xí)）已知函數(shù)SKIPIF1<0，若不等式SKIPIF1<0在區(qū)間SKIPIF1<0上恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2021·黑龍江綏化·高三階段練習(xí)（理））已知SKIPIF1<0，則下列說法正確的是（

）A．當(dāng)SKIPIF1<0時，SKIPIF1<0有極大值點(diǎn)和極小值點(diǎn) B．當(dāng)SKIPIF1<0時，SKIPIF1<0無極大值點(diǎn)和極小值點(diǎn)C．當(dāng)SKIPIF1<0時，SKIPIF1<0有最大值 D．當(dāng)SKIPIF1<0時，SKIPIF1<0的最小值小于或等于04．（2022·全國·模擬預(yù)測）（多選題）已知SKIPIF1<0，則（

）A．當(dāng)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0時，SKIPIF1<0B．當(dāng)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0時，SKIPIF1<0C．當(dāng)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0時，SKIPIF1<0D．當(dāng)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0時，SKIPIF1<05．（2022·廣東佛山·三模）已知函數(shù)SKIPIF1<0，其中SKIPIF1<0，SKIPIF1<0．(1)討論SKIPIF1<0的單調(diào)性；(2)當(dāng)SKIPIF1<0時，SKIPIF1<0是SKIPIF1<0的零點(diǎn)，過點(diǎn)SKIPIF1<0作曲線SKIPIF1<0的切線SKIPIF1<0，試證明直線SKIPIF1<0也是曲線SKIPIF1<0的切線．【典例3】根據(jù)函數(shù)的單調(diào)性求參數(shù)1．（2022·福建南平·三模）對任意的SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·高三專題練習(xí)）若函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）在區(qū)間SKIPIF1<0內(nèi)單調(diào)遞增，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2020·天津市第八中學(xué)高三期中）若函數(shù)SKIPIF1<0是SKIPIF1<0上的單調(diào)函數(shù)，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．（2018·浙江·模擬預(yù)測）若定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0的導(dǎo)函數(shù)SKIPIF1<0的圖象如圖所示，記SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·山東省淄博實(shí)驗中學(xué)高三期末）已知函數(shù)SKIPIF1<0(1)求函數(shù)SKIPIF1<0的極值；(2)設(shè)SKIPIF1<0，SKIPIF1<0為兩個不等的正數(shù)，且SKIPIF1<0，若不等式SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍．【典例4】函數(shù)單調(diào)性的應(yīng)用1．（2022·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0有兩個不同的零點(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<02．（2022·全國·模擬預(yù)測）若關(guān)于x的不等式SKIPIF1<0在SKIPIF1<0上恒成立，則實(shí)數(shù)m的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0，若SKIPIF1<0有解，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·山東威?！と＃┮阎瘮?shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時，求SKIPIF1<0的單調(diào)區(qū)間；(2)若SKIPIF1<0有兩個極值點(diǎn)SKIPIF1<0，且SKIPIF1<