新高考數(shù)學(xué)二輪復(fù)習(xí)分層訓(xùn)練專題10 導(dǎo)數(shù)在函數(shù)中的應(yīng)用（原卷版）

答案第=page11頁，共=sectionpages22頁專題10導(dǎo)數(shù)在函數(shù)中的應(yīng)用【練基礎(chǔ)】一、單選題1．（2023·云南昆明·昆明一中?？寄M預(yù)測）函數(shù)SKIPIF1<0，則滿足不等式SKIPIF1<0的實(shí)數(shù)x的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023·浙江·永嘉中學(xué)校聯(lián)考模擬預(yù)測）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0（SKIPIF1<0為自然對數(shù)的底數(shù)），則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023·甘肅蘭州·校考一模）已知SKIPIF1<0是偶函數(shù)，在(－∞，0)上滿足SKIPIF1<0恒成立，則下列不等式成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2023·內(nèi)蒙古赤峰·統(tǒng)考模擬預(yù)測）已知函數(shù)SKIPIF1<0存在唯一的極值點(diǎn)，則實(shí)數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023·全國·模擬預(yù)測）函數(shù)SKIPIF1<0恰有3個(gè)零點(diǎn)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2023·四川德陽·統(tǒng)考一模）函數(shù)SKIPIF1<0的大致圖像為（

）A． B．C． D．7．（2022·四川達(dá)州·統(tǒng)考一模）曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線平分圓SKIPIF1<0，則（

）A．SKIPIF1<0有兩個(gè)零點(diǎn)B．SKIPIF1<0有極大值C．SKIPIF1<0在SKIPIF1<0上為增函數(shù)D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<08．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0有四個(gè)不同的零點(diǎn)，從小到大依次為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．（2023·江蘇泰州·泰州中學(xué)?？家荒＃┮阎瘮?shù)SKIPIF1<0的導(dǎo)函數(shù)SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0是函數(shù)SKIPIF1<0的一個(gè)極大值點(diǎn)B．SKIPIF1<0C．函數(shù)SKIPIF1<0在SKIPIF1<0處切線的斜率小于零D．SKIPIF1<010．（2023·全國·高三專題練習(xí)）已知m，n關(guān)于x方程SKIPIF1<0的兩個(gè)根，且SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<011．（2023春·湖北襄陽·高三襄陽市襄州區(qū)第一高級中學(xué)校考開學(xué)考試）已知函數(shù)SKIPIF1<0，SKIPIF1<0是SKIPIF1<0的導(dǎo)數(shù)，下列說法正確的是（

）A．曲線SKIPIF1<0在SKIPIF1<0處的切線方程為SKIPIF1<0B．SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，在SKIPIF1<0上單調(diào)遞減C．對于任意的SKIPIF1<0總滿足SKIPIF1<0D．直線SKIPIF1<0與SKIPIF1<0在SKIPIF1<0上有一個(gè)交點(diǎn)且橫坐標(biāo)取值范圍為SKIPIF1<012．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，則下列結(jié)論正確的是（

）A．當(dāng)m＞0時(shí)，函數(shù)SKIPIF1<0的圖象在點(diǎn)SKIPIF1<0處的切線的斜率為SKIPIF1<0B．當(dāng)m＝l時(shí)，函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減C．當(dāng)m＝l時(shí)，函數(shù)SKIPIF1<0的最小值為1D．若SKIPIF1<0對SKIPIF1<0恒成立，則SKIPIF1<0三、填空題13．（2023·廣西柳州·統(tǒng)考模擬預(yù)測）①SKIPIF1<0，②SKIPIF1<0，③SKIPIF1<0，④SKIPIF1<0，上述不等式正確的有______（填序號）14．（2023·上海靜安·統(tǒng)考一模）已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0只有一個(gè)零點(diǎn)SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍為________.15．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，若對SKIPIF1<0，都有SKIPIF1<0成立，則實(shí)數(shù)a的最大值為___________．16．（2022·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0，若存在唯一整數(shù)SKIPIF1<0，使得SKIPIF1<0成立，則實(shí)數(shù)a的取值范圍為______．四、解答題17．（2023·云南昆明·昆明一中?？寄M預(yù)測）已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0且SKIPIF1<0存在零點(diǎn)，求實(shí)數(shù)a的取值范圍；(2)若SKIPIF1<0，求SKIPIF1<0的最大值.18．（2023·全國·高三專題練習(xí)）設(shè)函數(shù)SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)性；(2)當(dāng)SKIPIF1<0時(shí)，記SKIPIF1<0，是否存在整數(shù)t，使得關(guān)于x的不等式SKIPIF1<0有解?若存在，請求出t的最小值；若不存在，請說明理由.19．（2023·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的最小值；(2)設(shè)SKIPIF1<0，SKIPIF1<0，證明：SKIPIF1<0有且僅有SKIPIF1<0個(gè)零點(diǎn).（參考數(shù)據(jù)：SKIPIF1<0，SKIPIF1<0.）20．（2023·湖北·校聯(lián)考模擬預(yù)測）已知函數(shù)SKIPIF1<0.（注：SKIPIF1<0…是自然對數(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)m的取值范圍；(3)若存在SKIPIF1<0，對與任意的SKIPIF1<0，使得SKIPIF1<0恒成立，求SKIPIF1<0的最小值.【提能力】一、單選題21．（2023·全國·高三專題練習(xí)）設(shè)SKIPIF1<0，若SKIPIF1<0為函數(shù)SKIPIF1<0的極大值點(diǎn)，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<022．（2022·浙江·高三專題練習(xí)）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<023．（2021·江西宜春·統(tǒng)考模擬預(yù)測）“SKIPIF1<0”是“函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增”的（）A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分也不必要條件24．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<025．（2022·全國·高三專題練習(xí)）已知SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，其導(dǎo)函數(shù)為SKIPIF1<0且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<026．（2023·全國·高三專題練習(xí)）設(shè)函數(shù)SKIPIF1<0是奇函數(shù)SKIPIF1<0（SKIPIF1<0）的導(dǎo)函數(shù)，SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則使得SKIPIF1<0成立的SKIPIF1<0的取值范圍是A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<027．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，其中SKIPIF1<0，則（

）A．SKIPIF1<0在SKIPIF1<0上單調(diào)遞增 B．SKIPIF1<0在SKIPIF1<0上單調(diào)遞減C．曲線SKIPIF1<0是軸對稱圖形 D．曲線SKIPIF1<0是中心對稱圖形二、多選題(共0分)28．（2023春·山東濟(jì)寧·高三?？奸_學(xué)考試）已知函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0在SKIPIF1<0單調(diào)遞增B．SKIPIF1<0有兩個(gè)零點(diǎn)C．曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處切線的斜率為SKIPIF1<0D．SKIPIF1<0是偶函數(shù)29．（2022秋·黑龍江鶴崗·高三鶴崗一中?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0，則下列結(jié)論正確的是（

）A．函數(shù)SKIPIF1<0存在兩個(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．當(dāng)SKIPIF1<0時(shí)，方程SKIPIF1<0有且只有兩個(gè)實(shí)根D．若SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0的最小值為SKIPIF1<030．（2022春·全國·高三開學(xué)考試）關(guān)于函數(shù)SKIPIF1<0，下列判斷正確的是（

）A．SKIPIF1<0是SKIPIF1<0的極大值點(diǎn)B．函數(shù)SKIPIF1<0有且只有1個(gè)零點(diǎn)C．存在正實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0成立D．對任意兩個(gè)正實(shí)數(shù)SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0.31．（2021·吉林松原·?？既＃╆P(guān)于函數(shù)SKIPIF1<0，下列說法正確的是（

）A．SKIPIF1<0是SKIPIF1<0的極小值點(diǎn)；B．函數(shù)SKIPIF1<0有且只有1個(gè)零點(diǎn)；C．存在正整數(shù)SKIPIF1<0，使得SKIPIF1<0恒成立；D．對任意兩個(gè)正實(shí)數(shù)SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0.三、填空題(共0分)32．（2022·重慶北碚·西南大學(xué)附中校考模擬預(yù)測）函數(shù)SKIPIF1<0在SKIPIF1<0處取得極值10，則SKIPIF1<0___________.33．（2023·全國·高三專題練習(xí)）已知可導(dǎo)函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，滿足SKIPIF1<0，且SKIPIF1<0，則不等式SKIPIF1<0的解集是________．34．（2022秋·北京·高三北京市回民學(xué)校?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0，若存在SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的取值范圍是______.35．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，其中e是自然數(shù)對數(shù)的底數(shù)，若SKIPIF1<0，則實(shí)數(shù)a的取值范圍是_________．36．（2022春·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0（e為自然對數(shù)的底數(shù)），若關(guān)于x的方程SKIPIF1<0有且僅有四個(gè)不同的解，則實(shí)數(shù)k的取值范圍是______.四、解答題(共0分)37．（2021·全國·統(tǒng)考高考真題）已知函數(shù)SKIPIF1<0