新高考數(shù)學(xué)二輪復(fù)習(xí)重難點(diǎn)突破專題17 利用導(dǎo)數(shù)求函數(shù)的極值(原卷版)

專題17利用導(dǎo)數(shù)求函數(shù)的極值一、多選題1．下列命題正確的有（）A．已知SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0B．SKIPIF1<0，則SKIPIF1<0C．SKIPIF1<0的極大值和極小值的和為SKIPIF1<0D．過SKIPIF1<0的直線與函數(shù)SKIPIF1<0有三個(gè)交點(diǎn)，則該直線斜率的取值范圍是SKIPIF1<02．對(duì)于函數(shù)SKIPIF1<0，下列說法正確的是（）A．SKIPIF1<0在SKIPIF1<0處取得極大值SKIPIF1<0 B．SKIPIF1<0有兩個(gè)不同的零點(diǎn)C．SKIPIF1<0 D．若SKIPIF1<0在SKIPIF1<0上恒成立，則SKIPIF1<03．已知函數(shù)SKIPIF1<0，其導(dǎo)函數(shù)為SKIPIF1<0，下列命題中為真命題的是（）A．SKIPIF1<0的單調(diào)減區(qū)間是SKIPIF1<0B．SKIPIF1<0的極小值是﹣6C．過點(diǎn)SKIPIF1<0只能作一條直線與SKIPIF1<0的圖象相切D．SKIPIF1<0有且只有一個(gè)零點(diǎn)4．材料：函數(shù)是描述客觀世界變化規(guī)律的重要數(shù)學(xué)模型，在現(xiàn)行的高等數(shù)學(xué)與數(shù)學(xué)分析教材中，對(duì)“初等函數(shù)”給出了確切的定義，即由常數(shù)和基本初等函數(shù)經(jīng)過有限次的四則運(yùn)算及有限次的復(fù)合步驟所構(gòu)成的，且能用一個(gè)式子表示的，如函數(shù)SKIPIF1<0，我們可以作變形：SKIPIF1<0SKIPIF1<0，所以SKIPIF1<0可看作是由函數(shù)SKIPIF1<0和SKIPIF1<0復(fù)合而成的，即SKIPIF1<0為初等函數(shù).根據(jù)以上材料，對(duì)于初等函數(shù)SKIPIF1<0的說法正確的是（）A．無極小值 B．有極小值SKIPIF1<0 C．無極大值 D．有極大值SKIPIF1<05．設(shè)SKIPIF1<0為函數(shù)SKIPIF1<0的導(dǎo)函數(shù)，已知SKIPIF1<0，SKIPIF1<0，則下列結(jié)論不正確的是（）A．SKIPIF1<0在SKIPIF1<0單調(diào)遞增 B．SKIPIF1<0在SKIPIF1<0單調(diào)遞增C．SKIPIF1<0在SKIPIF1<0上有極大值SKIPIF1<0 D．SKIPIF1<0在SKIPIF1<0上有極小值SKIPIF1<06．已知函數(shù)SKIPIF1<0，其導(dǎo)函數(shù)為SKIPIF1<0，下列命題中真命題的為（）A．SKIPIF1<0的單調(diào)減區(qū)間是SKIPIF1<0B．SKIPIF1<0的極小值是SKIPIF1<0C．當(dāng)SKIPIF1<0時(shí)，對(duì)任意的SKIPIF1<0且SKIPIF1<0，恒有SKIPIF1<0（a）SKIPIF1<0（a）SKIPIF1<0D．函數(shù)SKIPIF1<0有且只有一個(gè)零點(diǎn)二、單選題7．設(shè)函數(shù)SKIPIF1<0在R上可導(dǎo)，其導(dǎo)函數(shù)為SKIPIF1<0，且函數(shù)SKIPIF1<0的圖象如圖所示，則下列結(jié)論中一定成立的是（）A．SKIPIF1<0有極大值SKIPIF1<0 B．SKIPIF1<0有極小值SKIPIF1<0C．SKIPIF1<0有極大值SKIPIF1<0 D．SKIPIF1<0有極小值SKIPIF1<08．下列關(guān)于函數(shù)SKIPIF1<0的結(jié)論中，正確結(jié)論的個(gè)數(shù)是（）①SKIPIF1<0的解集是SKIPIF1<0；②SKIPIF1<0是極大值，SKIPIF1<0是極小值；③SKIPIF1<0沒有最大值，也沒有最小值；④SKIPIF1<0有最大值，沒有最小值；⑤SKIPIF1<0有最小值，沒有最大值.A．1個(gè) B．2個(gè) C．3個(gè) D．4個(gè)9．函數(shù)y=f(x)的導(dǎo)函數(shù)y=f′(x)的圖象如圖所示，給出下列命題：①-3是函數(shù)y=f(x)的極值點(diǎn)；②y=f(x)在區(qū)間(-3，1)上單調(diào)遞增；③-1是函數(shù)y=f(x)的最小值點(diǎn)；④y=f(x)在x=0處切線的斜率小于零.以上正確命題的序號(hào)是（）A．①② B．③④ C．①③ D．②④10．已知函數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0零點(diǎn)的個(gè)數(shù)為（）A．1 B．2 C．3 D．411．設(shè)函數(shù)SKIPIF1<0，則（）A．SKIPIF1<0有極大值且為最大值 B．SKIPIF1<0有極小值，但無最小值C．若方程SKIPIF1<0恰有3個(gè)實(shí)根，則SKIPIF1<0 D．若方程SKIPIF1<0恰有一個(gè)實(shí)根，則SKIPIF1<0三、解答題12．已知函數(shù)SKIPIF1<0.（1）若SKIPIF1<0，求SKIPIF1<0在區(qū)間SKIPIF1<0上的極值；（2）討論函數(shù)SKIPIF1<0的單調(diào)性.13．設(shè)函數(shù)SKIPIF1<0.（1）當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0的極值；（2）若函數(shù)SKIPIF1<0有2個(gè)零點(diǎn)，求實(shí)數(shù)SKIPIF1<0的取值范圍.14．（1）已知SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，且SKIPIF1<0圖象在點(diǎn)SKIPIF1<0處的切線方程為SKIPIF1<0，求SKIPIF1<0的值.（2）求函數(shù)SKIPIF1<0在SKIPIF1<0上的極值.15．已知函數(shù)SKIPIF1<0.(1)若函數(shù)SKIPIF1<0，求函數(shù)SKIPIF1<0的極值；(2)若SKIPIF1<0在SKIPIF1<0時(shí)恒成立，求實(shí)數(shù)SKIPIF1<0的最小值.16．已知函數(shù)SKIPIF1<0，SKIPIF1<0（其中SKIPIF1<0）.（1）求函數(shù)SKIPIF1<0的極值；（2）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)有兩個(gè)零點(diǎn)，求正實(shí)數(shù)SKIPIF1<0的取值范圍；（3）求證：當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0.（說明：SKIPIF1<0是自然對(duì)數(shù)的底數(shù)，SKIPIF1<0）17．已知函數(shù)SKIPIF1<0，SKIPIF1<0．（1）設(shè)SKIPIF1<0，求函數(shù)SKIPIF1<0的極值；（2）若SKIPIF1<0，試研究函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù)．18．已知函數(shù)SKIPIF1<0，在SKIPIF1<0時(shí)取得極值.（1）求SKIPIF1<0的值；（2）求函數(shù)SKIPIF1<0的單調(diào)區(qū)間.19．已知函數(shù)SKIPIF1<0，SKIPIF1<0是奇函數(shù).（1）求SKIPIF1<0的表達(dá)式；（2）求函數(shù)SKIPIF1<0的極值.20．已知函數(shù)SKIPIF1<0.（1）當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0的極值；（2）當(dāng)SKIPIF1<0時(shí)，求不等式SKIPIF1<0的解集；（3）當(dāng)SKIPIF1<0時(shí)，若當(dāng)SKIPIF1<0，恒有SKIPIF1<0成立，求實(shí)數(shù)SKIPIF1<0的取值范圍.21．已知函數(shù)SKIPIF1<0(aSKIPIF1<0R).（1）討論SKIPIF1<0的極值；（2）若a＝2，且當(dāng)SKIPIF1<0時(shí)，不等式SKIPIF1<0恒成立，求實(shí)數(shù)m的取值范圍.22．已知函數(shù)SKIPIF1<0.（1）求SKIPIF1<0的極值；（2）若函數(shù)SKIPIF1<0在定義域內(nèi)有三個(gè)零點(diǎn)，求實(shí)數(shù)a的取值范圍.23．函數(shù)SKIPIF1<0.（1）求SKIPIF1<0的極大值和極小值；（2）已知SKIPIF1<0在區(qū)間D上的最大值為20，以下3個(gè)區(qū)間D的備選區(qū)間中，哪些是符合已知條件的？哪些不符合？請(qǐng)說明理由.①SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<024．已知函數(shù)SKIPIF1<0.（1）求函數(shù)SKIPIF1<0的極小值；（2）關(guān)于SKIPIF1<0的不等式SKIPIF1<0在SKIPIF1<0上存在解，求實(shí)數(shù)SKIPIF1<0的取值范圍.25．已知函數(shù)SKIPIF1<0.（Ⅰ）當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0的單調(diào)區(qū)間（Ⅱ）設(shè)SKIPIF1<0，若函數(shù)SKIPIF1<0在SKIPIF1<0有兩個(gè)零點(diǎn)，求SKIPIF1<0的取值范圍26．已知函數(shù)SKIPIF1<0的極大值為2.（1）求a的值和SKIPIF1<0的極小值；（2）求SKIPIF1<0在SKIPIF1<0處的切線方程.27．已知函數(shù)SKIPIF1<0.（1）討論SKIPIF1<0的極值；（2）若方程SKIPIF1<0在SKIPIF1<0上有實(shí)數(shù)解，求SKIPIF1<0的取值范圍.28．設(shè)函數(shù)SKIPIF1<0，其中SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0均為常數(shù)，曲線SKIPIF1<0在SKIPIF1<0處的切線方程為SKIPIF1<0.（1）求SKIPIF1<0，SKIPIF1<0