新高考數(shù)學(xué)一輪復(fù)習(xí)講與練第07講 一元函數(shù)的導(dǎo)數(shù)及其應(yīng)用（練）（原卷版）

第01講一元函數(shù)的導(dǎo)數(shù)及其應(yīng)用（一）1．若“SKIPIF1<0，使SKIPIF1<0成立”是假命題，則實(shí)數(shù)λ的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．若函數(shù)SKIPIF1<0，滿足SKIPIF1<0恒成立，則SKIPIF1<0的最大值為（

）A．3 B．4 C．SKIPIF1<0 D．SKIPIF1<03．下列求導(dǎo)運(yùn)算錯(cuò)誤的是（

）.A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．若函數(shù)SKIPIF1<0處有極大值，則常數(shù)SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05、在曲線SKIPIF1<0的所有切線中，與直線SKIPIF1<0平行的共有（

）．A．1條 B．2條 C．3條 D．4條6．已知SKIPIF1<0是函數(shù)SKIPIF1<0的導(dǎo)數(shù)，且SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則不等式SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)單調(diào)遞增，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知函數(shù)SKIPIF1<0，SKIPIF1<0，記SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．若SKIPIF1<0且SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<010．若函數(shù)SKIPIF1<0恰有2個(gè)不同的零點(diǎn)，則實(shí)數(shù)m的值是_________.11．已知函數(shù)SKIPIF1<0．(1)討論函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的單調(diào)性；(2)當(dāng)SKIPIF1<0時(shí)，證明：SKIPIF1<0．1．已知SKIPIF1<0，且滿足SKIPIF1<0，則下列正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0（多選）2．已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0可?。?/p>

）A．1 B．2 C．SKIPIF1<0 D．SKIPIF1<0（多選）3．已知SKIPIF1<0，函數(shù)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，下列說(shuō)法正確的是（

）A．SKIPIF1<0 B．單調(diào)遞增區(qū)間為SKIPIF1<0C．SKIPIF1<0的極大值為SKIPIF1<0 D．方程SKIPIF1<0有兩個(gè)不同的解4．已知正三棱錐的各頂點(diǎn)都在同一球面上，若該球的表面積為SKIPIF1<0，則該正三棱錐體積的最大值為___________.5．設(shè)SKIPIF1<0，則SKIPIF1<0的大小關(guān)系是___________.6．已知函數(shù)SKIPIF1<0，若關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是___________.7．過(guò)點(diǎn)SKIPIF1<0作曲線SKIPIF1<0的切線，若切線有且只有兩條，則實(shí)數(shù)SKIPIF1<0的取值范圍是___________.8．若函數(shù)SKIPIF1<0，則曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為___________.9．已知函數(shù)SKIPIF1<0(1)當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；(2)若函數(shù)SKIPIF1<0有3個(gè)不同零點(diǎn)，求實(shí)數(shù)SKIPIF1<0的取值范圍.10．已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0，求曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程；(2)若SKIPIF1<0，試討論函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù)．11．若SKIPIF1<0是函數(shù)SKIPIF1<0的極值點(diǎn)，則SKIPIF1<0______；SKIPIF1<0的極大值為______.1．（2022·全國(guó)·高考真題（理））當(dāng)SKIPIF1<0時(shí)，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．（2022·全國(guó)·高考真題（文））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．（2022·全國(guó)·高考真題（理））已知SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2010·全國(guó)·高考真題（文））若曲線y＝x2＋ax＋b在點(diǎn)(0，b)處的切線方程是x－y＋1＝0，則（

）A．a(chǎn)＝1，b＝1 B．a(chǎn)＝－1，b＝1C．a(chǎn)＝1，b＝－1 D．a(chǎn)＝－1，b＝－15．（2015·安徽·高考真題（文））函數(shù)f（x）＝ax3+bx2+cx+d的圖象如圖所示，則下列結(jié)論成立的是（

）A．a(chǎn)＞0，b＜0，c＞0，d＞0 B．a(chǎn)＞0，b＜0，c＜0，d＞0C．a(chǎn)＜0，b＜0，c＜0，d＞0 D．a(chǎn)＞0，b＞0，c＞0，d＜06．（2009·寧夏·高考真題（文））曲線SKIPIF1<0在點(diǎn)(0，1)處的切線方程為________．7．（2022·全國(guó)·高考真題（文））已知函數(shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的最大值；(2)若SKIPIF1<0恰有一個(gè)零點(diǎn)，求a的取值范圍．8．（2022·全國(guó)·高考真題（文））已知函數(shù)SKIPIF1<0，曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線也是曲線SKIPIF1<0的切線．(1)若SKIPIF1<0，求a；(2)求a的取值范圍．9．（2022·全國(guó)·高考真題（理））已知函數(shù)SKIPIF1<0