新高考數(shù)學(xué)一輪復(fù)習(xí)精講精練4.3 利用導(dǎo)數(shù)求極值最值（提升版）（原卷版）

4.3利用導(dǎo)數(shù)求極值最值（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)一無參函數(shù)的極值（點(diǎn)）【例1】（2022·天津市濱海新區(qū)塘沽第一中學(xué)）函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的極小值點(diǎn)是（

）A．0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·天津·耀華中學(xué)）已知曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線斜率為3，且SKIPIF1<0是SKIPIF1<0的極值點(diǎn)，則函數(shù)的另一個(gè)極值點(diǎn)為（

）A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．22．（2022·天津·崇化中學(xué)）函數(shù)SKIPIF1<0有（

）A．極大值為5，無極小值 B．極小值為SKIPIF1<0，無極大值C．極大值為5，極小值為SKIPIF1<0 D．極大值為5，極小值為SKIPIF1<03．（2022·重慶八中模擬預(yù)測）（多選）設(shè)函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，SKIPIF1<0是SKIPIF1<0的極小值點(diǎn)，以下結(jié)論一定正確的是（

）A．SKIPIF1<0是SKIPIF1<0的最小值點(diǎn)B．SKIPIF1<0是SKIPIF1<0的極大值點(diǎn)C．SKIPIF1<0是SKIPIF1<0的極大值點(diǎn)D．SKIPIF1<0是SKIPIF1<0的極大值點(diǎn)考點(diǎn)二已知極值（點(diǎn)）求參數(shù)【例2-1】（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上既有極大值又有極小值，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例2-2】（2022·陜西）已知函數(shù)SKIPIF1<0，若SKIPIF1<0是SKIPIF1<0的極小值點(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<0【一隅三反】1．（2022·廣東·惠來縣第一中學(xué)）若函數(shù)SKIPIF1<0在SKIPIF1<0處有極值，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．a(chǎn)不存在2．（2022·河南）已知函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)，則實(shí)數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·江西鷹潭）已知函數(shù)SKIPIF1<0的極大值點(diǎn)SKIPIF1<0，極小值點(diǎn)SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·河南洛陽·三模（理））若函數(shù)SKIPIF1<0在SKIPIF1<0上有且僅有6個(gè)極值點(diǎn)，則正整數(shù)SKIPIF1<0的值為（

）A．2 B．3 C．4 D．5考點(diǎn)三無參函數(shù)的最值【例3】（2022·全國·高考真題（文））函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0的最小值、最大值分別為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·海南華僑中學(xué)）已知函數(shù)SKIPIF1<0，下列說法正確的是（

）A．函數(shù)在SKIPIF1<0上遞增 B．函數(shù)無極小值C．函數(shù)只有一個(gè)極大值SKIPIF1<0 D．函數(shù)在SKIPIF1<0上最大值為32．（2022·四川省成都市新都一中）函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值為______．3．（2022·四川·威遠(yuǎn)中學(xué)校）對(duì)任意SKIPIF1<0，存在SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的最小值為_____.考點(diǎn)四已知最值求參數(shù)【例4-1】（2022·全國·高考真題（理））當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0取得最大值SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．1【例4-2】（2022·遼寧·大連二十四中模擬預(yù)測）若將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個(gè)單位，所得圖象對(duì)應(yīng)的函數(shù)在區(qū)間SKIPIF1<0上無極值點(diǎn)，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·江西省豐城中學(xué)模擬預(yù)測（文））已知函數(shù)SKIPIF1<0在SKIPIF1<0上有最小值，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·高三專題練習(xí)）已知不等式SKIPIF1<0對(duì)SKIPIF1<0恒成立，則實(shí)數(shù)a的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·河南洛陽）若曲線SKIPIF1<0與曲線：SKIPIF1<0=SKIPIF1<0SKIPIF1<0有公切線，則實(shí)數(shù)SKIPIF1<0的最大值為（

）A．SKIPIF1<0+SKIPIF1<0 B．SKIPIF1<0-SKIPIF1<0 C．SKIPIF1<0+SKIPIF1<0 D．SKIPIF1<0SKIPIF1<04（2022·吉林·延邊二中）若函數(shù)SKIPIF1<0最小值為SKIPIF1<0，SKIPIF1<0最小值為SKIPIF1<0，則SKIPIF1<0+SKIPIF1<0=（

）A．-2 B．0 C．2 D．-4考點(diǎn)五最值極值綜合運(yùn)用【例5】（2022·浙江嘉興）已知函數(shù)SKIPIF1<0．（注：SKIPIF1<0是自然對(duì)數(shù)的底數(shù)）(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只有一個(gè)極值點(diǎn)，求實(shí)數(shù)a的取值范圍；(3)若存在SKIPIF1<0，對(duì)與任意的SKIPIF1<0，使得SKIPIF1<0恒成立，求SKIPIF1<0的最小值．【一隅三反】1．（2022·河北·石家莊二中）已知函數(shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，證明：當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0；(2)若SKIPIF1<0，函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在極大值，求a的取值范圍．2．（2022·四川省成都市新都一中）已知函數(shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，若對(duì)任意SKIPIF1<0，SKIPIF1<0恒成立，求b的取值范圍；(2)若SKIPIF1<0，函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在極大值，求a的取值范圍．3．（2022·全國·哈師大附中）已知函數(shù)SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的導(dǎo)函數(shù)．(1)證明：當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0在區(qū)SKIPIF1<0內(nèi)存在唯一的極值點(diǎn)SKIPIF1<0，SKIPIF1<0；(2)若SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，求整數(shù)a的最小值．4.3利用導(dǎo)數(shù)求極值最值（精練）（提升版）題組一題組一無參函數(shù)的極值（點(diǎn)）1.（2022·山東·巨野縣實(shí)驗(yàn)中學(xué)）已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，導(dǎo)函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)的圖像如圖所示，則函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)的極小值有（

）A．1個(gè) B．2個(gè) C．3個(gè) D．4個(gè)2．（2022·天津?qū)嶒?yàn)中學(xué)）下列函數(shù)中存在極值點(diǎn)的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·福建省連城縣第一中學(xué)）函數(shù)SKIPIF1<0的極值點(diǎn)的個(gè)數(shù)是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．無數(shù)個(gè)4．（2022·全國·哈師大附中）已知SKIPIF1<0是函數(shù)SKIPIF1<0的一個(gè)極值點(diǎn)，則SKIPIF1<0的值是（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·遼寧·鞍山市華育高級(jí)中學(xué)）已知函數(shù)SKIPIF1<0的導(dǎo)函數(shù)SKIPIF1<0的圖像如圖所示，則下列判斷正確的是（

）A．在區(qū)間SKIPIF1<0上，SKIPIF1<0是增函數(shù) B．在區(qū)間SKIPIF1<0上，SKIPIF1<0是減函數(shù)C．SKIPIF1<0為SKIPIF1<0的極小值點(diǎn) D．2為SKIPIF1<0的極大值點(diǎn)6．（2022·湖北·南漳縣第一中學(xué)）函數(shù)SKIPIF1<0的極大值為（

）A．-2 B．2 C．SKIPIF1<0 D．不存在7（2022·天津河北）設(shè)SKIPIF1<0是函數(shù)f（x）的導(dǎo)函數(shù)，若函數(shù)f（x）的圖象如圖所示，則下列說法錯(cuò)誤的是（

）A．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0 B．當(dāng)SKIPIF1<0或SKIPIF1<0時(shí)，SKIPIF1<0C．當(dāng)SKIPIF1<0或SKIPIF1<0時(shí)，SKIPIF1<0 D．函數(shù)f（x）在SKIPIF1<0處取得極小值題組二題組二已知極值（點(diǎn)）求參數(shù)1．（2022·山東濰坊）已知函數(shù)SKIPIF1<0的圖像與直線SKIPIF1<0有3個(gè)不同的交點(diǎn)，則實(shí)數(shù)m的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·重慶·萬州純陽中學(xué)校）若函數(shù)SKIPIF1<0在SKIPIF1<0上存在唯一極值點(diǎn)，則實(shí)數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·四川省成都市新都一中）已知SKIPIF1<0沒有極值，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·湖北）函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)存在極值點(diǎn)，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<05．（2022·河南）已知函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2022·安徽·蒙城第一中學(xué)）已知SKIPIF1<0為常數(shù)，函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)，其中一個(gè)極值點(diǎn)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07（2022·陜西·長安一中）已知在SKIPIF1<0中，三個(gè)內(nèi)角SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的對(duì)邊分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，若函數(shù)SKIPIF1<0無極值點(diǎn)，則角B的最大值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022·四川·綿陽中學(xué)實(shí)驗(yàn)學(xué)校）若函數(shù)SKIPIF1<0在SKIPIF1<0處有極值10，則SKIPIF1<0（

）A．6 B．SKIPIF1<0 C．SKIPIF1<0或15 D．6或SKIPIF1<09．（2022·青?！ご笸ɑ刈逋磷遄灾慰h教學(xué)研究室二模（理））設(shè)函數(shù)SKIPIF1<0，則下列不是函數(shù)SKIPIF1<0極大值點(diǎn)的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2022·全國·高三專題練習(xí)）已知t和SKIPIF1<0是函數(shù)SKIPIF1<0的零點(diǎn)，且SKIPIF1<0也是函數(shù)SKIPIF1<0的極小值點(diǎn)，則SKIPIF1<0的極大值為（

）A．1 B．4 C．SKIPIF1<0 D．SKIPIF1<011．（2022·廣西·高三階段練習(xí)（理））已知函數(shù)SKIPIF1<0在其定義域的一個(gè)子區(qū)間SKIPIF1<0上有極值，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．（2022·安徽·合肥市第八中學(xué)）已知函數(shù)SKIPIF1<0在SKIPIF1<0處取極小值，且SKIPIF1<0的極大值為4，則SKIPIF1<0（

）A．-1 B．2 C．-3 D．413．（2022·河北承德）已知SKIPIF1<0是函數(shù)SKIPIF1<0的極值點(diǎn)，則SKIPIF1<0的極大值為_____．14．（2022·北京·101中學(xué)）設(shè)SKIPIF1<0是函數(shù)SKIPIF1<0的兩個(gè)極值點(diǎn)，若SKIPIF1<0，則實(shí)數(shù)a的取值范圍是______．15．（2022·浙江寧波）已知函數(shù)SKIPIF1<0，若SKIPIF1<0是函數(shù)SKIPIF1<0的唯一極值點(diǎn)，則實(shí)數(shù)k的取值范圍是_______．題組三題組三無參函數(shù)的最值1．（2022·海南華僑中學(xué)）已知函數(shù)SKIPIF1<0，下列說法正確的是（

）A．函數(shù)在SKIPIF1<0上遞增 B．函數(shù)無極小值C．函數(shù)只有一個(gè)極大值SKIPIF1<0 D．函數(shù)在SKIPIF1<0上最大值為32．（2022·湖北·模擬預(yù)測）SKIPIF1<0，SKIPIF1<0的最小值為___________．3．（2022·江蘇·南京市江寧高級(jí)中學(xué)模擬預(yù)測）若函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)有且只有一個(gè)零點(diǎn)，則SKIPIF1<0在SKIPIF1<0上的最大值與最小值的和為_______．4．（2022·全國·高三專題練習(xí)）若實(shí)數(shù)a、b、c、d滿足SKIPIF1<0，則SKIPIF1<0的最小值為______．5．（2022·四川省成都市新都一中）函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值為______．6．（2022·天津?qū)嶒?yàn)中學(xué)）函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值為__________．7．（2022·四川·威遠(yuǎn)中學(xué)校）對(duì)任意SKIPIF1<0，存在SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的最小值為_____.8．（2022·河南開封）已知SKIPIF1<0是奇函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的最小值為________．題組四題組四已知最值求參數(shù)1．（2022·江西萍鄉(xiāng)·三模）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0，對(duì)任意SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，都有SKIPIF1<0，若存在SKIPIF1<0，使不等式SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·遼寧·鞍山市華育高級(jí)中學(xué)）已知SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，則當(dāng)SKIPIF1<0取得最小值時(shí)，SKIPIF1<0所在區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·河南·模擬預(yù)測（理））已知函數(shù)SKIPIF1<0至多有2個(gè)不同的零點(diǎn)，則實(shí)數(shù)a的最大值為（

）．A．0 B．1 C．2 D．e4．（2022·遼寧·遼師大附中）設(shè)函數(shù)SKIPIF1<0(n為正整數(shù))，則SKIPIF1<0在[0，1]上的最大值為（

）A．0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·河南安陽）已知函數(shù)SKIPIF1<0，若SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0處取得最大值，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·江西）設(shè)兩個(gè)實(shí)數(shù)a，b滿足：SKIPIF1<0，則正整數(shù)n的最大值為（

）．（參考數(shù)據(jù)：SKIPIF1<0）A．7 B．8 C．9 D．10題組五題組五最值極值的綜合運(yùn)用1．（2022·浙江·寧波市李惠利中學(xué)）（多選）對(duì)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(gè)零點(diǎn)1和SKIPIF1<02．（2022·福建泉州）（多選）函數(shù)SKIPIF1<0在SKIPIF1<0處取得極大值，則a的值可以是（

）A．-1 B．0 C．3 D．43．（2022·黑龍江·哈爾濱市第六中學(xué)校）（多選）已知函數(shù)SKIPIF1<0，下列命題正確的是（

）A．若SKIPIF1<0是函數(shù)SKIPIF1<0的極值點(diǎn)，則SKIPIF1<0B．若SKIPIF1<0是函數(shù)SKIPIF1<0的極值點(diǎn)，則SKIPIF1<0在SKIPIF1<0上的最小值為SKIPIF1<0C．若SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則SKIPIF1<0D．若SKIPIF1<0在SKIPIF1<0上恒成立，則SKIPIF1<0