新高考數(shù)學一輪復習第3章 第03講 導數(shù)與函數(shù)的極值 最值 精講+精練（學生版）

第03講導數(shù)與函數(shù)的極值、最值(精講+精練）目錄第一部分：知識點精準記憶第二部分：課前自我評估測試第三部分：典型例題剖析高頻考點一：函數(shù)圖象與極值（點）的關系高頻考點二：求已知函數(shù)的極值（點）高頻考點三：根據(jù)函數(shù)的極值（點）求參數(shù)高頻考點四：求函數(shù)的最值（不含參）高頻考點五：求函數(shù)的最值（含參）高頻考點六：根據(jù)函數(shù)的最值求參數(shù)高頻考點七：函數(shù)的單調(diào)性、極值、最值的綜合應用第四部分：高考真題感悟第五部分：第03講導數(shù)與函數(shù)的極值、最值（精練）第一部分：知識點精準記憶第一部分：知識點精準記憶1、函數(shù)的極值一般地，對于函數(shù)SKIPIF1<0，（1）若在點SKIPIF1<0處有SKIPIF1<0，且在點SKIPIF1<0附近的左側有SKIPIF1<0，右側有SKIPIF1<0，則稱SKIPIF1<0為SKIPIF1<0的極小值點，SKIPIF1<0叫做函數(shù)SKIPIF1<0的極小值.（2）若在點SKIPIF1<0處有SKIPIF1<0，且在點SKIPIF1<0附近的左側有SKIPIF1<0，右側有SKIPIF1<0，則稱SKIPIF1<0為SKIPIF1<0的極大值點，SKIPIF1<0叫做函數(shù)SKIPIF1<0的極大值．（3）極小值點與極大值點通稱極值點，極小值與極大值通稱極值.注：極大（小）值點，不是一個點，是一個數(shù).2、函數(shù)的最大（?。┲狄话愕兀绻趨^(qū)間SKIPIF1<0上函數(shù)SKIPIF1<0的圖象是一條連續(xù)不斷的曲線，那么它必有最大值與最小值.設函數(shù)SKIPIF1<0在SKIPIF1<0上連續(xù)，在SKIPIF1<0內(nèi)可導，求SKIPIF1<0在SKIPIF1<0上的最大值與最小值的步驟為：（1）求SKIPIF1<0在SKIPIF1<0內(nèi)的極值；（2）將函數(shù)SKIPIF1<0的各極值與端點處的函數(shù)值SKIPIF1<0，SKIPIF1<0比較，其中最大的一個是最大值，最小的一個是最小值.3、函數(shù)的最值與極值的關系（1）極值是對某一點附近(即局部)而言，最值是對函數(shù)的定義區(qū)間SKIPIF1<0的整體而言；（2）在函數(shù)的定義區(qū)間SKIPIF1<0內(nèi)，極大（?。┲悼赡苡卸鄠€（或者沒有），但最大（?。┲抵挥幸粋€（或者沒有）；（3）函數(shù)SKIPIF1<0的極值點不能是區(qū)間的端點，而最值點可以是區(qū)間的端點；（4）對于可導函數(shù)，函數(shù)的最大(小)值必在極大(小)值點或區(qū)間端點處取得.第二部分：課前自我評估測試第二部分：課前自我評估測試一、判斷題1．（2021·全國·高二課前預習）函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上連續(xù)，則SKIPIF1<0在區(qū)間SKIPIF1<0上一定有最值，但不一定有極值.()2．（2021·全國·高二課前預習）函數(shù)的最大值不一定是函數(shù)的極大值.()3．（2021·全國·高二課前預習）函數(shù)的極大值一定大于極小值.()4．（2021·全國·高二課前預習）有極值的函數(shù)一定有最值，有最值的函數(shù)不一定有極值.()二、單選題1．（2022·廣東·高州市長坡中學高二階段練習）函數(shù)SKIPIF1<0在閉區(qū)間SKIPIF1<0上的最大值、最小值分別是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·黑龍江·牡丹江市第三高級中學高二期末）函數(shù)y＝SKIPIF1<0的最大值為（

）A．e－1 B．e C．e2 D．103．（2022·河北邢臺·高二階段練習）已知函數(shù)SKIPIF1<0的導函數(shù)的圖象如圖所示，則SKIPIF1<0極值點的個數(shù)為（

）A．4 B．5 C．6 D．74．（2022·天津市濱海新區(qū)塘沽第一中學高二階段練習）若函數(shù)SKIPIF1<0在SKIPIF1<0處取得極值，則SKIPIF1<0（

）A．1 B．2 C．3 D．4第三部分：典型例題剖析第三部分：典型例題剖析高頻考點一：函數(shù)圖象與極值（點）的關系1．（2022·黑龍江·牡丹江市第三高級中學高二開學考試）已知函數(shù)SKIPIF1<0的導函數(shù)SKIPIF1<0的圖像如圖所示，則下列結論正確的是（

）A．當SKIPIF1<0時，函數(shù)SKIPIF1<0取得極小值B．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是單調(diào)遞增的C．當SKIPIF1<0時，函數(shù)SKIPIF1<0取得極大值D．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是單調(diào)遞增的2．（2022·全國·高三專題練習）設函數(shù)SKIPIF1<0的導函數(shù)為SKIPIF1<0，函數(shù)SKIPIF1<0的圖像如圖所示，則（

）A．SKIPIF1<0的極大值為SKIPIF1<0，極小值為SKIPIF1<0B．SKIPIF1<0的極大值為SKIPIF1<0，極小值為SKIPIF1<0C．SKIPIF1<0的極大值為SKIPIF1<0，極小值為SKIPIF1<0D．SKIPIF1<0的極大值為SKIPIF1<0，極小值為SKIPIF1<03．（2022·寧夏·銀川二中高二期末（文））已知函數(shù)SKIPIF1<0的導函數(shù)SKIPIF1<0的圖象如圖所示，則下列結論正確的是（

）.A．函數(shù)SKIPIF1<0在SKIPIF1<0上是增函數(shù)B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0是函數(shù)SKIPIF1<0的極小值點4．（2022·全國·高二）如圖是函數(shù)SKIPIF1<0的大致圖象，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0高頻考點二：求已知函數(shù)的極值（點）1．（2022·山東師范大學附中高二階段練習）函數(shù)SKIPIF1<0，SKIPIF1<0有（

）A．極大值25，極小值SKIPIF1<0 B．極大值25，極小值SKIPIF1<0C．極大值25，無極小值 D．極小值SKIPIF1<0，無極大值2．（2022·江蘇·海門中學高二期末）已知函數(shù)SKIPIF1<0在SKIPIF1<0處取得極值，則SKIPIF1<0的極大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·高二）已知函數(shù)SKIPIF1<0，則SKIPIF1<0在定義域上（

）A．有極小值SKIPIF1<0 B．有極大值SKIPIF1<0 C．有最大值 D．無最小值4．（2022·全國·高二）函數(shù)SKIPIF1<0的極大值與極小值之和為（

）A．SKIPIF1<0 B．3 C．SKIPIF1<0 D．SKIPIF1<05．（2022·全國·高二課時練習）若SKIPIF1<0是函數(shù)SKIPIF1<0的極值點，則函數(shù)SKIPIF1<0（

）A．有極小值1 B．有極大值1 C．有極小值-1 D．有極大值-1高頻考點三：根據(jù)函數(shù)的極值（點）求參數(shù)1．（2022·河南新鄉(xiāng)·二模（文））已知SKIPIF1<0，函數(shù)SKIPIF1<0的極小值為SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·高三專題練習）已知SKIPIF1<0在SKIPIF1<0處取得極值，則SKIPIF1<0的最小值為___________.3．（2022·全國·高三專題練習）若函數(shù)SKIPIF1<0不存在極值點，則SKIPIF1<0的取值范圍是______．4．（2022·江西南昌·高二期末（文））已知函數(shù)SKIPIF1<0在SKIPIF1<0處有極值2，則SKIPIF1<0______.5．（2022·全國·高二課時練習）函數(shù)SKIPIF1<0在x＝1處有極值為10，則b的值為__.6．（2022·四川省綿陽南山中學高二階段練習（文））若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有兩個極值點，則實數(shù)a的取值范圍是______．7．（2022·寧夏·平羅中學高二期末（文））若函數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0有極值SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的解析式；(2)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間.高頻考點四：求函數(shù)的最值（不含參）1．（2022·四川·攀枝花七中高二階段練習（理））已知SKIPIF1<0是SKIPIF1<0的極值點，則SKIPIF1<0在SKIPIF1<0上的最大值是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（多選）（2022·山東省東明縣第一中學高二階段練習）函數(shù)SKIPIF1<0在SKIPIF1<0上的最值情況為（

）A．最大值為12 B．最大值為5C．最小值為SKIPIF1<0 D．最小值為SKIPIF1<03．（2022·福建·啟悟中學高二階段練習）已知函數(shù)SKIPIF1<0(1)求SKIPIF1<0在SKIPIF1<0處的切線方程；(2)求SKIPIF1<0在SKIPIF1<0上的最值．4．（2022·廣東·深圳市南山區(qū)華僑城中學高二階段練習）已知關于x的函數(shù)SKIPIF1<0，且函數(shù)f（x）在SKIPIF1<0處有極值－SKIPIF1<0．(1)求實數(shù)b，c的值；(2)求函數(shù)f（x）在[－1，2]上的最大值和最小值．5．（2022·廣東·高州市長坡中學高二階段練習）已知函數(shù)SKIPIF1<0．（SKIPIF1<0為常數(shù)）(1)當SKIPIF1<0時，求函數(shù)SKIPIF1<0的最值；6．（2022·遼寧·朝陽市第二高級中學高二階段練習）已知SKIPIF1<0．(1)若SKIPIF1<0在SKIPIF1<0處取得極值，求SKIPIF1<0的最小值；7．（2022·江蘇·常熟中學高二階段練習）已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，求SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值；高頻考點五：求函數(shù)的最值（含參）1．（2022·廣西·高二期末（文））已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，討論函數(shù)SKIPIF1<0的單調(diào)性；(2)當SKIPIF1<0時，求SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值和最大值.2．（2022·北京市朝陽區(qū)人大附中朝陽分校模擬預測）設函數(shù)SKIPIF1<0.(1)求曲線SKIPIF1<0在SKIPIF1<0處的切線方程；(2)若函數(shù)SKIPIF1<0有最大值并記為SKIPIF1<0，求SKIPIF1<0的最小值；3．（2022·河南·模擬預測（理））已知函數(shù)SKIPIF1<0.(1)當SKIPIF1<0時，判斷函數(shù)SKIPIF1<0的單調(diào)性；(2)證明函數(shù)SKIPIF1<0存在最小值SKIPIF1<0，并求出函數(shù)SKIPIF1<0的最大值.4．（2022·山東·菏澤一中高二階段練習）已知函數(shù)SKIPIF1<0，SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；(2)求SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值.5．（2022·河南·模擬預測（文））已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0僅有一個零點，求a的取值范圍；(2)若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值與最小值之差為SKIPIF1<0，求SKIPIF1<0的最小值．高頻考點六：根據(jù)函數(shù)的最值求參數(shù)1．（2022·河南·模擬預測（文））已知函數(shù)SKIPIF1<0無最大值，則實數(shù)a的取值范圍是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·陜西安康·高二期末（文））已知SKIPIF1<0，函數(shù)SKIPIF1<0的最小值為SKIPIF1<0，則SKIPIF1<0（

）A．1或2 B．2 C．1或3 D．2或33．（2022·河南開封·高二階段練習（理））已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有最小值，則實數(shù)a的取值范圍是______．4．（2022·河北·武安市第三中學高二階段練習）已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0，求SKIPIF1<0的極值；(2)若SKIPIF1<0在SKIPIF1<0上的最大值為SKIPIF1<0，求實數(shù)SKIPIF1<0的值．5．（2022·福建·福鼎市第一中學高二階段練習）已知函數(shù)SKIPIF1<0(1)討論SKIPIF1<0在定義域內(nèi)的單調(diào)性；(2)若SKIPIF1<0，且SKIPIF1<0在SKIPIF1<0上的最小值為SKIPIF1<0，求實數(shù)SKIPIF1<0的值.6．（2022·河南·洛寧縣第一高級中學高二階段練習（文））已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0在SKIPIF1<0上不單調(diào)，求a的取值范圍；(2)若SKIPIF1<0的最小值為SKIPIF1<0，求a的值.7．（2022·全國·高二單元測試）已知函數(shù)SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；(2)函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值小于零，求a的取值范圍．高頻考點七：函數(shù)的單調(diào)性、極值、最值的綜合應用1．（2022·全國·高二）已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0在SKIPIF1<0上存在最小值，則a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·內(nèi)蒙古·海拉爾第二中學高三階段練習（文））函數(shù)SKIPIF1<0有極小值，且極小值為0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·高三專題練習）已知函數(shù)SKIPIF1<0在SKIPIF1<0處取得極小值SKIPIF1<0，且SKIPIF1<0在區(qū)間SKIPIF1<0上存在最小值，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國·高三專題練習（理））若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在最小值，則實數(shù)m的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·河南焦作·二模（文））已知函數(shù)SKIPIF1<0.(1)求SKIPIF1<0的極值；(2)若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上沒有極值，求實數(shù)k的取值范圍.6．（2022·重慶市育才中學模擬預測）已知函數(shù)SKIPIF1<0，其中SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)性；(2)證明：SKIPIF1<0是函數(shù)SKIPIF1<0存在最小值的充分而不必要條件.7．（2022·全國·高二課時練習）已知函數(shù)SKIPIF1<0，(1)討論函數(shù)SKIPIF1<0的極值情況；(2)求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值.第四部分：高考真題感悟第四部分：高考真題感悟1．（2021·全國·高考真題（理））設SKIPIF1<0，若SKIPIF1<0為函數(shù)SKIPIF1<0的極大值點，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2021·北京·高考真題）已知函數(shù)SKIPIF1<0．（1）若SKIPIF1<0，求曲線SKIPIF1<0在點SKIPIF1<0處的切線方程；（2）若SKIPIF1<0在SKIPIF1<0處取得極值，求SKIPIF1<0的單調(diào)區(qū)間，以及其最大值與最小值．3．（2021·全國·高考真題（文））設函數(shù)SKIPIF1<0，其中SKIPIF1<0.（1）討論SKIPIF1<0的單調(diào)性；（2）若SKIPIF1<0的圖象與SKIPIF1<0軸沒有公共點，求a的取值范圍.4．（2020·北京·高考真題）已知函數(shù)SKIPIF1<0．（Ⅰ）求曲線SKIPIF1<0的斜率等于SKIPIF1<0的切線方程；（Ⅱ）設曲線SKIPIF1<0在點SKIPIF1<0處的切線與坐標軸圍成的三角形的面積為SKIPIF1<0，求SKIPIF1<0的最小值．5．（2020·全國·高考真題（文））已知函數(shù)f（x）=2lnx+1．（1）若f（x）≤2x+c，求c的取值范圍；（2）設a>0時，討論函數(shù)g（x）=SKIPIF1<0的單調(diào)性．第五部分：第03講導數(shù)與函數(shù)的極值、最值（精練）第五部分：第03講導數(shù)與函數(shù)的極值、最值（精練）一、單選題1．（2022·甘肅省民樂縣第一中學高二階段練習（理））已知函數(shù)SKIPIF1<0在SKIPIF1<0處有極小值，則實數(shù)m的值為（）A．3 B．－1或－3 C．－1 D．－32．（2022·天津市濱海新區(qū)塘沽第一中學高二階段練習）函數(shù)SKIPIF1<0的定義域為開區(qū)間SKIPIF1<0，導函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)的圖象如圖所示，則函數(shù)SKIPIF1<0在開區(qū)間SKIPIF1<0內(nèi)有極小值點（

）A．1個 B．2個 C．3個 D．4個3．（2022·河北·武安市第三中學高二階段練習）函數(shù)SKIPIF1<0的極值點為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·河南·欒川縣第一高級中學高二階段練習（理））已知函數(shù)SKIPIF1<0在SKIPIF1<0上不存在極值點，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·福建省漳州第一中學高二階段練習）函數(shù)SKIPIF1<0在區(qū)間(0，e](其中e為自然對數(shù)的底數(shù))上的最大值為（

）A．SKIPIF1<0 B．－1 C．－e D．06．（2022·福建·福鼎市第一中學高二階段練習）函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有最大值，則m的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．（2022·陜西商洛·一模（理））若對任意的SKIPIF1<0，恒有SKIPIF1<0，則a的取值范圍為（

）A．（—∞，e] B．SKIPIF1<0C．（—∞，SKIPIF1<0] D．[SKIPIF