新高考數(shù)學(xué)二輪復(fù)習(xí)培優(yōu)專題訓(xùn)練專題10 導(dǎo)數(shù)的綜合運(yùn)用（原卷版）

專題10導(dǎo)數(shù)的綜合運(yùn)用1、【2022年全國乙卷】已知x=x1和x=x2分別是函數(shù)f(x)=2ax?ex2、【2021年新高考2卷】已知函數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0的圖象在點(diǎn)SKIPIF1<0和點(diǎn)SKIPIF1<0的兩條切線互相垂直，且分別交y軸于M，N兩點(diǎn)，則SKIPIF1<0取值范圍是_______．3、（2023年新課標(biāo)全國Ⅰ卷）1．已知函數(shù)SKIPIF1<0．(1)討論SKIPIF1<0的單調(diào)性；(2)證明：當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0．4、（2023年新課標(biāo)全國Ⅱ卷）（1）證明：當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0；（2）已知函數(shù)SKIPIF1<0，若SKIPIF1<0是SKIPIF1<0的極大值點(diǎn)，求a的取值范圍．5、（2023年全國乙卷數(shù)學(xué)（理））8．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)是否存在a，b，使得曲線SKIPIF1<0關(guān)于直線SKIPIF1<0對(duì)稱，若存在，求a，b的值，若不存在，說明理由.(3)若SKIPIF1<0在SKIPIF1<0存在極值，求a的取值范圍.6、【2022年全國甲卷】已知函數(shù)fx(1)若fx≥0，求(2)證明：若fx有兩個(gè)零點(diǎn)x1,7、【2022年全國乙卷】已知函數(shù)f(1)當(dāng)a=1時(shí)，求曲線y=fx在點(diǎn)0,f(2)若fx在區(qū)間?1,0,0,+題組一、函數(shù)的零點(diǎn)、極值點(diǎn)的綜合性問題1-1、（2022·湖北·黃石市有色第一中學(xué)高三期末）（多選題）設(shè)函數(shù)fx=xlnA．不等式gx>0的解集為B．函數(shù)在0,e單調(diào)遞增，在e,+C．當(dāng)x∈1e,1D．若函數(shù)Fx=f1-2、（2023·江蘇連云港·統(tǒng)考模擬預(yù)測）已知函數(shù)SKIPIF1<0．(1)求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值；(2)若關(guān)于SKIPIF1<0的方程SKIPIF1<0有兩個(gè)不相等的實(shí)數(shù)根，求實(shí)數(shù)SKIPIF1<0的取值范圍．1-3、（2022·河北深州市中學(xué)高三期末）已知函數(shù)SKIPIF1<0．(1)證明：函數(shù)SKIPIF1<0在SKIPIF1<0上存在唯一的零點(diǎn)；(2)若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值為1，求a的值．題組二、利用導(dǎo)數(shù)研究不等式及證明問題2-1、（2023·江蘇徐州·徐州市第七中學(xué)?？家荒＃┮阎瘮?shù)SKIPIF1<0.(1)若SKIPIF1<0且函數(shù)SKIPIF1<0在SKIPIF1<0上是單調(diào)遞增函數(shù)，求SKIPIF1<0的取值范圍；(2)設(shè)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，若SKIPIF1<0滿足SKIPIF1<0，證明：SKIPIF1<0.2-2、（2023·江蘇南通·統(tǒng)考一模）已知函數(shù)SKIPIF1<0和SKIPIF1<0有相同的最大值.(1)求實(shí)數(shù)SKIPIF1<0；(2)設(shè)直線SKIPIF1<0與兩條曲線SKIPIF1<0和SKIPIF1<0共有四個(gè)不同的交點(diǎn)，其橫坐標(biāo)分別為SKIPIF1<0，證明：SKIPIF1<0.2-3、（2023·江蘇南通·統(tǒng)考模擬預(yù)測）設(shè)函數(shù)SKIPIF1<0，SKIPIF1<0.(1)若函數(shù)SKIPIF1<0圖象恰與函數(shù)SKIPIF1<0圖象相切，求實(shí)數(shù)SKIPIF1<0的值；(2)若函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)SKIPIF1<0，SKIPIF1<0，設(shè)點(diǎn)SKIPIF1<0，SKIPIF1<0，證明：SKIPIF1<0、SKIPIF1<0兩點(diǎn)連線的斜率SKIPIF1<0.2-4、（2023·江蘇南京·南京市秦淮中學(xué)校考模擬預(yù)測）已知函數(shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，討論SKIPIF1<0的單調(diào)性；(2)當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，求a的取值范圍；(3)設(shè)SKIPIF1<0，證明：SKIPIF1<0．題組三、利用導(dǎo)數(shù)研究含參問題3-1、（2023·江蘇泰州·泰州中學(xué)?？家荒＃┮阎瘮?shù)SKIPIF1<0（SKIPIF1<0為自然對(duì)數(shù)的底數(shù)）.(1)若不等式SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍；(2)若不等式SKIPIF1<0在SKIPIF1<0上恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍.3-2、（2023·江蘇南京·?？家荒＃┮阎瘮?shù)SKIPIF1<0(其中SKIPIF1<0為自然對(duì)數(shù)的底數(shù)).（1）當(dāng)SKIPIF1<0時(shí)，求證：函數(shù)SKIPIF1<0圖象上任意一點(diǎn)處的切線斜率均大于SKIPIF1<0；（2）若SKIPIF1<0對(duì)于任意的SKIPIF1<0，SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍.3-3、（2023·云南曲靖·統(tǒng)考一模）已知函數(shù)SKIPIF1<0的圖像與直線l：SKIPIF1<0相切于點(diǎn)SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的圖像在點(diǎn)SKIPIF1<0處的切線在x軸上的截距；(2)求c與a的函數(shù)關(guān)系SKIPIF1<0；(3)當(dāng)a為函數(shù)g（a）的零點(diǎn)時(shí)，若對(duì)任意SKIPIF1<0，不等式SKIPIF1<0恒成立．求實(shí)數(shù)k的最值．1、（2023·黑龍江·黑龍江實(shí)驗(yàn)中學(xué)?？家荒＃┰O(shè)函數(shù)SKIPIF1<0.(1)若曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線斜率為SKIPIF1<0，求SKIPIF1<0的值；(2)若SKIPIF1<0存在兩個(gè)極值點(diǎn)SKIPIF1<0，且對(duì)任意SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍.2、（2023·吉林通化·梅河口市第五中學(xué)校考一模）已知SKIPIF1<0SKIPIF1<0．(1)求證：當(dāng)x>0時(shí)，SKIPIF1<0(2)若不等式SKIPIF1<0，（其中SKIPIF1<0）恒成立時(shí)，實(shí)數(shù)m的取值范圍為（-∞，t]，求證：SKIPIF1<0．3、（2023·黑龍江大慶·統(tǒng)考一模）已知函數(shù)SKIPIF1<0的兩個(gè)不同極值點(diǎn)分別為SKIPIF1<0，SKIPIF1<0（SKIPIF1<0）.(1)求實(shí)數(shù)SKIPIF1<0的取值范圍；(2)證明：SKIPIF1<0（SKIPIF1<0為自然對(duì)數(shù)的底數(shù)）.4、（2023·四川廣安·四川省廣安友誼中學(xué)校考模擬預(yù)測）已知函數(shù)SKIPIF1<0．(1)若函數(shù)SKIPIF1<0