新高考數(shù)學(xué)二輪復(fù)習(xí)培優(yōu)專題訓(xùn)練專題09 利用導(dǎo)數(shù)研究函數(shù)的性質(zhì)（原卷版）

專題09利用導(dǎo)數(shù)研究函數(shù)的性質(zhì)1、（2023年全國(guó)甲卷數(shù)學(xué)（文））曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02、（2023年新課標(biāo)全國(guó)Ⅱ卷）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則a的最小值為（

）．A．SKIPIF1<0 B．e C．SKIPIF1<0 D．SKIPIF1<03、（2023年新課標(biāo)全國(guó)Ⅱ卷）（多選題）．若函數(shù)SKIPIF1<0既有極大值也有極小值，則（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04、（2023年全國(guó)乙卷數(shù)學(xué)（文））函數(shù)SKIPIF1<0存在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<05、（2023年全國(guó)乙卷數(shù)學(xué)（理））設(shè)SKIPIF1<0，若函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則a的取值范圍是______.6、【2022年新高考2卷】曲線y=ln7、【2022年新高考1卷】（多選題）已知函數(shù)f(x)=xA．f(x)有兩個(gè)極值點(diǎn) B．f(x)有三個(gè)零點(diǎn)C．點(diǎn)(0,1)是曲線y=f(x)的對(duì)稱中心 D．直線y=2x是曲線y=f(x)的切線8、（2023年全國(guó)乙卷數(shù)學(xué)（文））．已知函數(shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，求曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程．(2)若函數(shù)SKIPIF1<0在SKIPIF1<0單調(diào)遞增，求SKIPIF1<0的取值范圍．題組一、函數(shù)圖像的切線問(wèn)題1-1、（2023·重慶·統(tǒng)考三模）已知直線y＝ax－a與曲線SKIPIF1<0相切，則實(shí)數(shù)a＝（

）A．0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<01-2、（2023·江蘇南京·校考一模）若直線SKIPIF1<0與曲線SKIPIF1<0相切，則SKIPIF1<0_________．1-3、（2023·黑龍江大慶·統(tǒng)考一模）函數(shù)SKIPIF1<0的圖象在點(diǎn)SKIPIF1<0處的切線方程為______．1-4、（2023·吉林通化·梅河口市第五中學(xué)?？家荒＃┤糁本€SKIPIF1<0是函數(shù)SKIPIF1<0的圖象在某點(diǎn)處的切線，則實(shí)數(shù)SKIPIF1<0______．1-5、（2023·河北唐山·統(tǒng)考三模）已知曲線SKIPIF1<0與SKIPIF1<0有公共切線，則實(shí)數(shù)SKIPIF1<0的取值范圍為__________.題組二、利用導(dǎo)數(shù)研究函數(shù)的最值、極值與零點(diǎn)問(wèn)題2-1、（2022·江蘇蘇州·高三期末）（多選題）已知函數(shù)SKIPIF1<0，則（）A．SKIPIF1<0，函數(shù)SKIPIF1<0在SKIPIF1<0上均有極值B．SKIPIF1<0，使得函數(shù)SKIPIF1<0在SKIPIF1<0上無(wú)極值C．SKIPIF1<0，函數(shù)SKIPIF1<0在SKIPIF1<0上有且僅有一個(gè)零點(diǎn)D．SKIPIF1<0，使得函數(shù)SKIPIF1<0在SKIPIF1<0上有兩個(gè)零點(diǎn)2-2、（2022·江蘇海門·高三期末）已知函數(shù)SKIPIF1<0有三個(gè)零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．(0，SKIPIF1<0) B．[0，SKIPIF1<0) C．[0，SKIPIF1<0] D．(0，SKIPIF1<0)2-3、（2023·山西運(yùn)城·統(tǒng)考三模）（多選題）已知函數(shù)SKIPIF1<0，則下列說(shuō)法正確的是（

）A．曲線SKIPIF1<0在SKIPIF1<0處的切線與直線SKIPIF1<0垂直B．SKIPIF1<0在SKIPIF1<0上單調(diào)遞增C．SKIPIF1<0的極小值為SKIPIF1<0D．SKIPIF1<0在SKIPIF1<0上的最小值為SKIPIF1<02-4、（2023·山西晉中·統(tǒng)考三模）設(shè)SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02-5、（2023·安徽黃山·統(tǒng)考三模）已知定義域?yàn)镾KIPIF1<0的函數(shù)SKIPIF1<0，其導(dǎo)函數(shù)為SKIPIF1<0，且滿足SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0題組三、利用導(dǎo)數(shù)研究函數(shù)性質(zhì)的綜合性問(wèn)題3-1、（2022·江蘇通州·高三期末）（多選題）已知函數(shù)f(x)＝ekx，g(x)＝SKIPIF1<0，其中k≠0，則（）A．若點(diǎn)P(a，b)在f(x)的圖象上，則點(diǎn)Q(b，a)在g(x)的圖象上B．當(dāng)k＝e時(shí)，設(shè)點(diǎn)A，B分別在f(x)，g(x)的圖象上，則|AB|的最小值為SKIPIF1<0C．當(dāng)k＝1時(shí)，函數(shù)F(x)＝f(x)－g(x)的最小值小于SKIPIF1<0D．當(dāng)k＝－2e時(shí)，函數(shù)G(x)＝f(x)－g(x)有3個(gè)零點(diǎn)3-2、（2023·浙江溫州·統(tǒng)考三模）（多選題）已知函數(shù)SKIPIF1<0，其中SKIPIF1<0是其圖象上四個(gè)不重合的點(diǎn)，直線SKIPIF1<0為函數(shù)SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線，則（

）A．函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0中心對(duì)稱B．函數(shù)SKIPIF1<0的極大值有可能小于零C．對(duì)任意的SKIPIF1<0，直線SKIPIF1<0的斜率恒大于直線SKIPIF1<0的斜率D．若SKIPIF1<0三點(diǎn)共線，則SKIPIF1<0.3-3、（2023·江蘇南京·校考一模）（多選題）定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，則下列說(shuō)法正確的是（

）A．SKIPIF1<0在SKIPIF1<0處取得極大值，極大值為SKIPIF1<0B．SKIPIF1<0有兩個(gè)零點(diǎn)C．若SKIPIF1<0在SKIPIF1<0上恒成立，則SKIPIF1<0D．SKIPIF1<01、（2023·江蘇南京·南京市秦淮中學(xué)校考模擬預(yù)測(cè)）設(shè)a為實(shí)數(shù)，函數(shù)SKIPIF1<0的導(dǎo)函數(shù)是SKIPIF1<0，且SKIPIF1<0是偶函數(shù)，則曲線SKIPIF1<0在原點(diǎn)處的切線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02、（2023·山東聊城·統(tǒng)考三模）若直線SKIPIF1<0與曲線SKIPIF1<0相切，則SKIPIF1<0的最大值為（）A．0 B．1 C．2 D．SKIPIF1<03、（2023·江蘇徐州·徐州市第七中學(xué)?？家荒＃┮阎猄KIPIF1<0，SKIPIF1<0，SKIPIF1<0（其中SKIPIF1<0為自然常數(shù)），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<04、（2023·江蘇泰州·泰州中學(xué)?？家荒＃ǘ噙x題）已知函數(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<05、（2023·江蘇徐州·徐州市第七中學(xué)校考一模）（多選題）已知SKIPIF1<0,SKIPIF1<0，下列說(shuō)法正確的是