新高考數(shù)學(xué)一輪復(fù)習(xí)精講精練9.6 導(dǎo)數(shù)的綜合運(yùn)用（基礎(chǔ)版）（原卷版）

9.6導(dǎo)數(shù)的綜合運(yùn)用（精講）（基礎(chǔ)版）思維導(dǎo)圖思維導(dǎo)圖考點(diǎn)呈現(xiàn)考點(diǎn)呈現(xiàn)例題剖析例題剖析考點(diǎn)一零點(diǎn)問題【例1】（2022·全國(guó)·成都七中）設(shè)函數(shù)SKIPIF1<0?為常數(shù)).(1)討論SKIPIF1<0?的單調(diào)性；(2)討論函數(shù)SKIPIF1<0?的零點(diǎn)個(gè)數(shù).【一隅三反】1．（2022·全國(guó)·興國(guó)中學(xué)）已知函數(shù)SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間，(2)若函數(shù)SKIPIF1<0有三個(gè)零點(diǎn)，求實(shí)數(shù)m的取值范圍．2．（2022·黑龍江）已知函數(shù)SKIPIF1<0，SKIPIF1<0，曲線SKIPIF1<0和SKIPIF1<0在原點(diǎn)處有相同的切線.(1)求SKIPIF1<0的值；(2)判斷函數(shù)SKIPIF1<0在SKIPIF1<0上零點(diǎn)的個(gè)數(shù)，并說明理由.3．（2022·河南）已知SKIPIF1<0.SKIPIF1<0(1)討論SKIPIF1<0的單調(diào)性；(2)若SKIPIF1<0有一個(gè)零點(diǎn)，求k的取值范圍.考點(diǎn)二不等式成立【例2】（2022·江西南昌）已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0，求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；(2)若不等式SKIPIF1<0在區(qū)間SKIPIF1<0上有解，求實(shí)數(shù)SKIPIF1<0的取值范圍．【例2-2】（2022·四川成都）已知函數(shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，求證：SKIPIF1<0；(2)當(dāng)SKIPIF1<0時(shí)，不等式SKIPIF1<0恒成立，求a的取值范圍．【一隅三反】1．（2022·甘肅定西）已知函數(shù)SKIPIF1<0，SKIPIF1<0(1)求SKIPIF1<0在SKIPIF1<0處的切線方程(2)若存在SKIPIF1<0時(shí)，使SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍．2．（2022·四川眉山）已知SKIPIF1<0.(1)求SKIPIF1<0的極值點(diǎn)；(2)若不等式SKIPIF1<0存在正數(shù)解，求實(shí)數(shù)SKIPIF1<0的取值范圍.3．（2022·廣東廣州·一模）已知函數(shù)SKIPIF1<0，SKIPIF1<0.(1)若函數(shù)SKIPIF1<0只有一個(gè)零點(diǎn)，求實(shí)數(shù)a的取值所構(gòu)成的集合；(2)若函數(shù)SKIPIF1<0恒成立，求實(shí)數(shù)a的取值范圍.考點(diǎn)三雙變量【例3】（2022·全國(guó)·成都七中高三開學(xué)考試（理））設(shè)函數(shù)SKIPIF1<0（SKIPIF1<0?為常數(shù)）.(1)討論SKIPIF1<0?的單調(diào)性；(2)若函數(shù)SKIPIF1<0?有兩個(gè)不相同的零點(diǎn)SKIPIF1<0?，證明:SKIPIF1<0?.【一隅三反】1．（2022·福建泉州·模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0(1)討論SKIPIF1<0的單調(diào)性；(2)若SKIPIF1<0在SKIPIF1<0有兩個(gè)極值點(diǎn)SKIPIF1<0，求證：SKIPIF1<0．2．（2022·四川·高三開學(xué)考試（理））已知函數(shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，求證：SKIPIF1<0；(2)當(dāng)SKIPIF1<0時(shí)，已知SKIPIF1<0，SKIPIF1<0是兩個(gè)不相等的正數(shù)且SKIPIF1<0，求證：SKIPIF1<0．8．（2022·全國(guó)·興國(guó)中學(xué)高三階段練習(xí)（理））已知函數(shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，求實(shí)數(shù)m的取值范圍；(2)若SKIPIF1<0，使得SKIPIF1<0，求證：SKIPIF1<0．4．（2022·河南·鄭州市第七中學(xué)高三階段練習(xí)（理））巳知函數(shù)SKIPIF1<0.(1)求函數(shù)f（x）的最大值;(2)若關(guān)于x的方程SKIPIF1<0有兩個(gè)不等實(shí)數(shù)根SKIPIF1<0證明:SKIPIF1<0SKIPIF1<09.6導(dǎo)數(shù)的綜合運(yùn)用（精練）（基礎(chǔ)版）題組一題組一零點(diǎn)問題1．（2022·內(nèi)蒙古包頭·高三開學(xué)考試（理））已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0，求SKIPIF1<0的單調(diào)區(qū)間；(2)討論SKIPIF1<0的零點(diǎn)情況．2．（2020·陜西·榆林市第十中學(xué)高三期中（理））已知函數(shù)SKIPIF1<0，SKIPIF1<0.(1)討論SKIPIF1<0的單調(diào)性；(2)設(shè)SKIPIF1<0，函數(shù)SKIPIF1<0有兩個(gè)不同的零點(diǎn)，求實(shí)數(shù)SKIPIF1<0的取值范圍.3．（2022·廣東·金山中學(xué)高三階段練習(xí)）已知函數(shù)SKIPIF1<0，和SKIPIF1<0，(1)若SKIPIF1<0與SKIPIF1<0有相同的最小值，求SKIPIF1<0的值；(2)設(shè)SKIPIF1<0有兩個(gè)零點(diǎn)，求SKIPIF1<0的取值范圍．4．（2022·安徽省定遠(yuǎn)縣第三中學(xué)高三階段練習(xí)）已知函數(shù)SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的導(dǎo)數(shù)．(1)判斷并證明SKIPIF1<0在區(qū)間SKIPIF1<0上存在的極大值點(diǎn)個(gè)數(shù)；(2)判斷SKIPIF1<0的零點(diǎn)個(gè)數(shù)．題組二題組二不等式成立1．（2022·廣東汕頭·高三階段練習(xí)）已知函數(shù)SKIPIF1<0.(1)求SKIPIF1<0的單調(diào)區(qū)間；(2)當(dāng)SKIPIF1<0時(shí)，若SKIPIF1<0在SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍.2．（2022·河南·南陽(yáng)市第六完全學(xué)校高級(jí)中學(xué)高三階段練習(xí)（文））已知SKIPIF1<0.(1)當(dāng)SKIPIF1<0時(shí)，求曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程；(2)若SKIPIF1<0對(duì)SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍.3．（2023·全國(guó)·高三專題練習(xí)）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)若SKIPIF1<0對(duì)任意SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍．4．（2022·河南·商丘市第一高級(jí)中學(xué)高三開學(xué)考試（理））已知函數(shù)SKIPIF1<0.(1)若函數(shù)SKIPIF1<0有一個(gè)零點(diǎn)，求k的取值范圍；(2)已知函數(shù)SKIPIF1<0，若SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍.5．（2022·河南·滎陽(yáng)市教育體育局教學(xué)研究室高三開學(xué)考試）已知函數(shù)SKIPIF1<0，SKIPIF1<0（SKIPIF1<0）(1)求SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程(2)若對(duì)于任意的SKIPIF1<0，都有SKIPIF1<0成立，求實(shí)數(shù)SKIPIF1<0的取值范圍．6．（2022·北京·高三開學(xué)考試）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)間和極值；(2)若曲線SKIPIF1<0不存在斜率為－2的切線，求a的取值范圍；(3)當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0恒成立，求a的取值范圍.（只需直接寫出結(jié)論）題組三題組三雙變量1．（2022·黑龍江·高三開學(xué)考試）已知函數(shù)SKIPIF1<0存在兩個(gè)極值點(diǎn)SKIPIF1<0.(1)求SKIPIF1<0的取值范圍；(2)求SKIPIF1<0的最小值.2．（2022·河北省曲陽(yáng)縣第一高級(jí)中學(xué)高三階段練習(xí)）已知函數(shù)SKIPIF1<0.(1)求SKIPIF1<0的單調(diào)區(qū)間；(2)若SKIPIF1<0有兩個(gè)不同的零點(diǎn)SKIPIF1<0，證明：SKIPIF1<0.3．（2021·黑龍江·大慶實(shí)驗(yàn)中學(xué)高三開學(xué)考試（理））已知SKIPIF1<0，SKIPIF1<0為自然對(duì)數(shù)的底數(shù).(1)若SKIPIF1<0是SKIPIF1<0上的單調(diào)函數(shù)，求實(shí)數(shù)SKIPIF1<0的取值范圍；(2)當(dāng)SKIPIF1<0時(shí)，若SKIPIF1<0有兩個(gè)正極值點(diǎn)SKIPIF1<0，SKIPIF1<0，證明：SKIPIF1<0.4．（2023·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0時(shí)，SKIPIF1<0，求SKIPIF1<0的取值范圍；(2)當(dāng)SKIPIF1<0時(shí)，方程SKIPIF1<0有兩個(gè)不相等的實(shí)數(shù)根SKIPIF1<0，證明：SKIPIF1<0．5．（2022·四川涼山）已知函數(shù)SKIPIF1<0．(1)討論SKIPIF1<0的單調(diào)性；(2)證明：若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0．6．（2022·廣東·廣州市真光中學(xué)高三開學(xué)考試）已知函數(shù)SKIPIF1<0，SKIPIF1<0