新高考數(shù)學(xué)一輪復(fù)習(xí)提升訓(xùn)練4.5 導(dǎo)數(shù)的綜合運(yùn)用（精講）（原卷版）

4.5導(dǎo)數(shù)的綜合運(yùn)用（精講）（提升版）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)的個(gè)數(shù)【例1】（2022·廣東·深圳市光明區(qū)高級(jí)中學(xué)模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0的極值點(diǎn)；(2)當(dāng)SKIPIF1<0時(shí)，試討論函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù).【一隅三反】1．（2022·江蘇·南京市天印高級(jí)中學(xué)模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的圖象在SKIPIF1<0處的切線方程；(2)判斷函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù)，并說(shuō)明理由.2．（2022·北京四中三模）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)，討論SKIPIF1<0的零點(diǎn)個(gè)數(shù).3．（2022·云南師大附中高三階段練習(xí)（文））已知函數(shù)SKIPIF1<0.(1)討論SKIPIF1<0的單調(diào)性；(2)當(dāng)SKIPIF1<0時(shí)，設(shè)SKIPIF1<0，求證：SKIPIF1<0在SKIPIF1<0上只有1個(gè)零點(diǎn)考點(diǎn)二已知零點(diǎn)個(gè)數(shù)求參【例2】（2022·全國(guó)·高考真題）已知函數(shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的最大值；(2)若SKIPIF1<0恰有一個(gè)零點(diǎn)，求a的取值范圍．【一隅三反】1．（2022·河南·平頂山市第一高級(jí)中學(xué)模擬預(yù)測(cè)（理））已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0，討論SKIPIF1<0的單調(diào)性；(2)若SKIPIF1<0有兩個(gè)零點(diǎn)，求實(shí)數(shù)a的取值范圍．2（2022·全國(guó)·高考真題（理））已知函數(shù)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在區(qū)間SKIPIF1<0各恰有一個(gè)零點(diǎn)，求a的取值范圍．3．（2022·貴州·貴陽(yáng)一中高三階段練習(xí)（理））已知函數(shù)SKIPIF1<0(1)討論SKIPIF1<0的單調(diào)性；(2)當(dāng)SKIPIF1<0有三個(gè)零點(diǎn)時(shí)a的取值范圍恰好是SKIPIF1<0求b的值.考點(diǎn)三不等式恒（能）成立【例3】（2022·天津市）已知函數(shù)SKIPIF1<0，SKIPIF1<0（SKIPIF1<0），其中e是自然對(duì)數(shù)的底數(shù).(1)當(dāng)SKIPIF1<0時(shí)，（?。┣骃KIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程；（ⅱ）求SKIPIF1<0的最小值；(2)討論函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù)；(3)若存在SKIPIF1<0，使得SKIPIF1<0成立，求a的取值范圍【一隅三反】1．（2022·河南安陽(yáng)）已知函數(shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0在SKIPIF1<0處的切線方程；(2)對(duì)于SKIPIF1<0，不等式SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍．2．（2022·海南中學(xué)高三階段練習(xí)）已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，求SKIPIF1<0的單調(diào)區(qū)間；(2)是否存在實(shí)數(shù)a，使SKIPIF1<0對(duì)SKIPIF1<0恒成立，若存在，求出a的值或取值范圍；若不存在，請(qǐng)說(shuō)明理由.3．（2022·青?！ご笸ɑ刈逋磷遄灾慰h教學(xué)研究室三模（理））已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0在SKIPIF1<0上僅有一個(gè)零點(diǎn)，求實(shí)數(shù)a的取值范圍；(2)若對(duì)任意的SKIPIF1<0，SKIPIF1<0恒成立，求實(shí)數(shù)a的取值范圍．考點(diǎn)四證明不等式【例4】（2022·四川省）己知函數(shù)SKIPIF1<0（其中e為自然對(duì)數(shù)的底數(shù)，SKIPIF1<0…）．(1)若SKIPIF1<0恒成立，求實(shí)數(shù)a的值；(2)若SKIPIF1<0，求證：SKIPIF1<0．【一隅三反】1．（2022·四川省瀘縣第二中學(xué)模擬預(yù)測(cè)（理））已知函數(shù)SKIPIF1<0（e為自然對(duì)數(shù)的底數(shù)）有兩個(gè)零點(diǎn)．(1)若SKIPIF1<0，求SKIPIF1<0在SKIPIF1<0處的切線方程；(2)若SKIPIF1<0的兩個(gè)零點(diǎn)分別為SKIPIF1<0，證明：SKIPIF1<0．2．（2022·河南·高三階段練習(xí)）已知函數(shù)SKIPIF1<0.(1)求SKIPIF1<0的最小值；(2)證明：SKIPIF1<0.3．（2022·河南）已知函數(shù)SKIPIF1<0.(1)求SKIPIF1<0的最小值；(2)若SKIPIF1<0，證明：SKIPIF1<0.4．（2022·全國(guó)·高考真題）已知函數(shù)SKIPIF1<0