新高考數(shù)學(xué)一輪復(fù)習(xí) 第4章 導(dǎo)數(shù)及其應(yīng)用（綜合檢測(cè)）（原卷版）

第四章導(dǎo)數(shù)及其應(yīng)用綜合檢測(cè)（考試時(shí)間：120分鐘試卷滿分：150分）注意事項(xiàng)：1．答卷前，考生務(wù)必將自己的姓名、準(zhǔn)考證號(hào)等填寫在答題卡和試卷指定位置上。2．回答選擇題時(shí)，選出每小題答案后，用鉛筆把答題卡上對(duì)應(yīng)題目的答案標(biāo)號(hào)涂黑。如需改動(dòng)，用橡皮擦干凈后，再選涂其他答案標(biāo)號(hào)。回答非選擇題時(shí)，將答案寫在答題卡上。寫在本試卷上無效。3．考試結(jié)束后，將本試卷和答題卡一并交回。第Ⅰ卷一、單項(xiàng)選擇題：本題共8小題，每小題5分，共40分．在每小題給出的四個(gè)選項(xiàng)中，只有一項(xiàng)是符合題目要求.1．設(shè)SKIPIF1<0是函數(shù)SKIPIF1<0的導(dǎo)函數(shù)，SKIPIF1<0的圖象如圖所示，則SKIPIF1<0的圖象可能是（

）A． B．C． D．2．函數(shù)SKIPIF1<0在SKIPIF1<0處的切線的傾斜角為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．若函數(shù)SKIPIF1<0有極值點(diǎn)為0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．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<05．已知函數(shù)SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，恒有SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知奇函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的連續(xù)可導(dǎo)函數(shù)，其導(dǎo)函數(shù)是SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0恒成立，則下列不等關(guān)系一定正確的是A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知SKIPIF1<0是自然對(duì)數(shù)的底數(shù)，函數(shù)SKIPIF1<0，若整數(shù)m滿足SKIPIF1<0，則所有滿足條件的m的和為（

）A．0 B．13 C．21 D．30二、多項(xiàng)選擇題：本題共4小題，每小題5分，共20分.在每小題給出的選項(xiàng)中，有多項(xiàng)符合題目要求.全部選對(duì)的得5分，部分選對(duì)的得2分，有選錯(cuò)的得0分.9．已知定義在區(qū)間SKIPIF1<0上的函數(shù)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，SKIPIF1<0的圖象如圖所示，則（

）A．SKIPIF1<0在SKIPIF1<0上單調(diào)遞增B．曲線SKIPIF1<0在SKIPIF1<0處的切線的斜率為0C．SKIPIF1<0D．SKIPIF1<0有1個(gè)極大值點(diǎn)10．已知函數(shù)SKIPIF1<0，則下列結(jié)論正確的是（

）A．函數(shù)SKIPIF1<0存在三個(gè)不同的零點(diǎn)B．函數(shù)SKIPIF1<0既存在極大值又存在極小值C．若SKIPIF1<0時(shí)，SKIPIF1<0，則t的最小值為2D．當(dāng)SKIPIF1<0時(shí)，方程SKIPIF1<0有且只有兩個(gè)實(shí)根11．已知函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)SKIPIF1<0與SKIPIF1<0，且SKIPIF1<0，則下列結(jié)論正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<012．若直線SKIPIF1<0與兩曲線SKIPIF1<0、SKIPIF1<0分別交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，且曲線SKIPIF1<0在SKIPIF1<0點(diǎn)處的切線為SKIPIF1<0，曲線SKIPIF1<0在SKIPIF1<0點(diǎn)處的切線為SKIPIF1<0，則下列結(jié)論正確的有（

）A．存在SKIPIF1<0，使SKIPIF1<0 B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0取得最小值C．SKIPIF1<0沒有最小值 D．SKIPIF1<0第Ⅱ卷三、填空題：本題共4小題，每小題5分，共20分13．已知曲線SKIPIF1<0在SKIPIF1<0處的切線方程為SKIPIF1<0，則SKIPIF1<0________．14．若函數(shù)SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0___________.15．若曲線SKIPIF1<0有兩條過坐標(biāo)原點(diǎn)的切線，則a的取值范圍是________________．16．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_________．四、解答題：本小題共6小題，共70分，其中第17題10分，18~22題12分。解答應(yīng)寫出文字說明、證明過程或演算步驟.17．已知函數(shù)SKIPIF1<0，SKIPIF1<0．(1)討論SKIPIF1<0的單調(diào)性；(2)若SKIPIF1<0，探討函數(shù)SKIPIF1<0極值點(diǎn)的個(gè)數(shù)．18．已知函數(shù)SKIPIF1<0，SKIPIF1<0.(1)討論SKIPIF1<0的單調(diào)區(qū)間；(2)若SKIPIF1<0有3個(gè)零點(diǎn)，求SKIPIF1<0的取值范圍.19．已知函數(shù)SKIPIF1<0，SKIPIF1<0.（1）當(dāng)時(shí)SKIPIF1<0，若關(guān)于SKIPIF1<0的不等式SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍；（2）當(dāng)SKIPIF1<0時(shí)，證明：SKIPIF1<0SKIPIF1<0.20．已知函數(shù)SKIPIF1<0．(1)討論SKIPIF1<0的零點(diǎn)個(gè)數(shù)．(2)若SKIPIF1<0有兩個(gè)不同的零點(diǎn)SKIPIF1<0，證明：SKIPIF1<0．21．已知函數(shù)SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)性；(2)若SKIPIF1<0是函數(shù)SKIPIF1<0的兩個(gè)不同極值點(diǎn)，且滿足：SKIPIF1<0，求證：SKIPIF1<0.22．已知函