新高考數(shù)學一輪復習分層提升練習第16練 導數(shù)與函數(shù)的極值、最值（原卷版）

第16練導數(shù)與函數(shù)的極值、最值（精練）刷真題明導向刷真題明導向一、單選題1．當SKIPIF1<0時，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．12．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<03．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<04．已知正四棱錐的側棱長為l，其各頂點都在同一球面上.若該球的體積為SKIPIF1<0，且SKIPIF1<0，則該正四棱錐體積的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題5．已知函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0有兩個極值點 B．SKIPIF1<0有三個零點C．點SKIPIF1<0是曲線SKIPIF1<0的對稱中心 D．直線SKIPIF1<0是曲線SKIPIF1<0的切線三、填空題6．函數(shù)SKIPIF1<0的最小值為______.7．已知SKIPIF1<0和SKIPIF1<0分別是函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）的極小值點和極大值點．若SKIPIF1<0，則a的取值范圍是____________．四、解答題8．已知函數(shù)SKIPIF1<0．(1)當SKIPIF1<0時，求SKIPIF1<0的最大值；(2)若SKIPIF1<0恰有一個零點，求a的取值范圍．9．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．10．設函數(shù)SKIPIF1<0，已知SKIPIF1<0是函數(shù)SKIPIF1<0的極值點．（1）求a；（2）設函數(shù)SKIPIF1<0．證明:SKIPIF1<0．11．已知SKIPIF1<0，函數(shù)SKIPIF1<0．（I）求曲線SKIPIF1<0在點SKIPIF1<0處的切線方程：（II）證明SKIPIF1<0存在唯一的極值點（III）若存在a，使得SKIPIF1<0對任意SKIPIF1<0成立，求實數(shù)b的取值范圍．12．已知函數(shù)SKIPIF1<0和SKIPIF1<0有相同的最小值．(1)求a；(2)證明：存在直線SKIPIF1<0，其與兩條曲線SKIPIF1<0和SKIPIF1<0共有三個不同的交點，并且從左到右的三個交點的橫坐標成等差數(shù)列．【A組

在基礎中考查功底】一、單選題1．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．設SKIPIF1<0，若不等式SKIPIF1<0在SKIPIF1<0上恒成立，則實數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知函數(shù)SKIPIF1<0的導函數(shù)的圖像如圖所示，則下列結論正確的是（

）A．SKIPIF1<0是SKIPIF1<0的極小值點 B．SKIPIF1<0是SKIPIF1<0的極小值點C．SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減 D．曲線SKIPIF1<0在SKIPIF1<0處的切線斜率小于零4．若x＝a是函數(shù)SKIPIF1<0的極大值點，則a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)有極小值，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知函數(shù)SKIPIF1<0與SKIPIF1<0，則它們的圖象交點個數(shù)為（

）A．0 B．1 C．2 D．不確定7．SKIPIF1<0的最大值與最小值之差為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在最小值，則實數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．已知函數(shù)SKIPIF1<0（SKIPIF1<0為自然對數(shù)的底數(shù)），若SKIPIF1<0在SKIPIF1<0上恒成立，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題10．對于函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0有極大值，沒有極小值B．SKIPIF1<0有極小值，沒有極大值C．函數(shù)SKIPIF1<0與SKIPIF1<0的圖象有兩個交點D．函數(shù)SKIPIF1<0有兩個零點11．（多選）已知函數(shù)SKIPIF1<0，則下列結論正確的是（

）A．函數(shù)SKIPIF1<0存在三個不同的零點B．函數(shù)SKIPIF1<0既存在極大值又存在極小值C．若SKIPIF1<0時，SKIPIF1<0，則t的最小值為2D．當SKIPIF1<0時，方程SKIPIF1<0有且只有兩個實根12．已知SKIPIF1<0函數(shù)SKIPIF1<0的極值點，則（

）A．SKIPIF1<0是SKIPIF1<0的極小值點 B．SKIPIF1<0有三個零點C．SKIPIF1<0 D．SKIPIF1<013．已知函數(shù)SKIPIF1<0（e為自然對數(shù)的底數(shù)，SKIPIF1<0），則關于函數(shù)SKIPIF1<0，下列結論正確的是（

）A．有2個零點 B．有2個極值點 C．在SKIPIF1<0單調(diào)遞增 D．最小值為1三、填空題14．已知函數(shù)SKIPIF1<0存在極值點，則實數(shù)a的取值范圍是_____________．15．已知SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則實數(shù)SKIPIF1<0的取值范圍是__________.16．已知SKIPIF1<0，SKIPIF1<0是該函數(shù)的極值點，定義SKIPIF1<0表示超過實數(shù)x的最小整數(shù)，則SKIPIF1<0的值為______．17．已知函數(shù)SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0在SKIPIF1<0上恒成立，則實數(shù)SKIPIF1<0的取值范圍是___________.四、解答題18．）已知函數(shù)SKIPIF1<0，SKIPIF1<0.(1)求函數(shù)SKIPIF1<0的極值；(2)若對任意SKIPIF1<0，都有SKIPIF1<0成立，求SKIPIF1<0的取值范圍.19．已知函數(shù)f(x)=x-mlnx-m.(1)討論函數(shù)f(x)的單調(diào)性；(2)若函數(shù)f(x)有最小值g(m)，證明：g(m)SKIPIF1<0在SKIPIF1<0上恒成立.20．已知函數(shù)SKIPIF1<0，其中SKIPIF1<0．(1)討論SKIPIF1<0的單調(diào)性；(2)若SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的最大值．21．已知函數(shù)SKIPIF1<0，SKIPIF1<0.(1)判斷函數(shù)SKIPIF1<0的單調(diào)性，并求其最值；(2)若SKIPIF1<0恒成立，求實數(shù)SKIPIF1<0的取值范圍.22．已知三次函數(shù)SKIPIF1<0的極大值是SKIPIF1<0，其導函數(shù)SKIPIF1<0的圖象經(jīng)過點SKIPIF1<0，如圖所示，求(1)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的值；(2)若函數(shù)SKIPIF1<0有三個零點，求SKIPIF1<0的取值范圍．【B組】一、單選題1．已知SKIPIF1<0，函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0有最小值，有最大值 B．SKIPIF1<0無最小值，有最大值C．SKIPIF1<0有最小值，無最大值 D．SKIPIF1<0無最小值，無最大值2．函數(shù)SKIPIF1<0在SKIPIF1<0上有唯一的極大值，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．）如圖所示，太極圖是由黑白兩個魚形紋組成的圖案，俗稱陰陽魚，太極圖展現(xiàn)了一種相互轉(zhuǎn)化，相對統(tǒng)一的和諧美，若函數(shù)SKIPIF1<0的圖象能將圓的周長和面積同時等分成兩個部分，則稱SKIPIF1<0為這個圓的一個“太極函數(shù)”．已知函數(shù)SKIPIF1<0是圓SKIPIF1<0的一個太極函數(shù)，若函數(shù)SKIPIF1<0有兩個極值點，則實數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．）已知SKIPIF1<0，且SKIPIF1<0，則實數(shù)t的最小值為（

）A．1 B．SKIPIF1<0 C．2 D．SKIPIF1<05．已知SKIPIF1<0，設函數(shù)SKIPIF1<0，若關于x的不等式SKIPIF1<0在SKIPIF1<0上恒成立，則a的取值范圍為（

）A．0，,e2 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．）已知函數(shù)SKIPIF1<0圖象的相鄰兩條對稱軸間的距離為SKIPIF1<0，函數(shù)SKIPIF1<0（SKIPIF1<0是SKIPIF1<0的導數(shù)）的圖象關于原點對稱，若SKIPIF1<0在SKIPIF1<0上恰有3個極值點，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題7．已知函數(shù)SKIPIF1<0則（

）A．SKIPIF1<0沒有極值點B．當SKIPIF1<0時，函數(shù)SKIPIF1<0圖像與直線y＝m有三個公共點C．點SKIPIF1<0是曲線SKIPIF1<0的對稱中心D．直線SKIPIF1<0是曲線SKIPIF1<0的切線8．設函數(shù)SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的導函數(shù)，則（

）A．SKIPIF1<0有唯一的零點和極值點，且零點小于極值點B．曲線SKIPIF1<0在點SKIPIF1<0處的切線斜率為SKIPIF1<0C．SKIPIF1<0為偶函數(shù)D．SKIPIF1<0在SKIPIF1<0時值域為SKIPIF1<09．已知函數(shù)SKIPIF1<0，若SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的可能的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、填空題10．已知函數(shù)SKIPIF1<0在定義域內(nèi)不存在極值點，則實數(shù)a的取值范圍是______．11．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在最大值，則實數(shù)SKIPIF1<0的取值范圍是__________.12．已知函數(shù)SKIPIF1<0有兩個極值點SKIPIF1<0和SKIPIF1<0，則實數(shù)a的取值范圍為______.13．）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上最大值為SKIPIF1<0，最小值為SKIPIF1<0，則實數(shù)SKIPIF1<0__________．14．）已知函數(shù)SKIPIF1<0和SKIPIF1<0的表達式分別為SKIPIF1<0，SKIPIF1<0，若對任意SKIPIF1<0，若存在SKIPIF1<0，使得SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍是__________.四、解答題15．已知函數(shù)SKIPIF1<0.(1)當SKIPIF1<0時，（ⅰ）求曲線SKIPIF1<0在點SKIPIF1<0處的切線方程；（ⅱ）求證：SKIPIF1<0，SKIPIF1<0.(2)若SKIPIF1<0在SKIPIF1<0上恰有一個極值點，求SKIPIF1<0的取值范圍.16．已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0，求SKIPIF1<0的極值；(2)若SKIPIF1<0在區(qū)間SKIPIF1<0上有兩個零點，求實數(shù)a的取值范圍．17．已知函數(shù)SKIPIF1<0.(1)當SKIPIF1<0時，求SKIPIF1<0在點SKIPIF1<0處的切線方程；(2)當SKIPIF1<0時，求證：SKIPIF1<0.18．已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，關于x的不等式SKIPIF1<0恰有兩個整數(shù)解，求m的取值范圍；(2)若SKIPIF1<0的最小值為1，求a.19．已知SKIPIF1<0(1)若SKIPIF1<0，討論SKIPIF1<0的單調(diào)性；(2)當SKIPIF1<0時，SKIPIF1<0的最小值為SKIPIF1<0，求SKIPIF1<0的取值范圍.【C組】一、單選題1．若SKIPIF1<0，則a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．對于兩個函數(shù)SKIPIF1<0與SKIPIF1<0，若這兩個函數(shù)值相等時對應的自變量分別為SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．-1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．）若函數(shù)SKIPIF1<0有兩個極值點SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知函數(shù)SKIPIF1<0有兩個極值點，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題5．已知SKIPIF1<0，若關于SKIPIF1<0的方程SKIPIF1<0存在正零點，則實數(shù)SKIPIF1<0的值可