試卷第=page11頁(yè)，共=sectionpages33頁(yè)專題32導(dǎo)數(shù)大題綜合1．（2023·遼寧沈陽(yáng)·統(tǒng)考一模）已知SKIPIF1<0，SKIPIF1<0．(1)討論SKIPIF1<0的單調(diào)性；(2)若SKIPIF1<0有兩個(gè)零點(diǎn)，求a的值．2．（2023秋·浙江寧波·高三期末）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)若對(duì)SKIPIF1<0恒成立，求k的取值范圍；(3)求證：對(duì)SKIPIF1<0，不等式SKIPIF1<0恒成立.3．（2023秋·浙江嘉興·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0.(1)若曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線與兩坐標(biāo)軸圍成的三角形的面積為SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的值；(2)證明：若SKIPIF1<0，則SKIPIF1<0.4．（2020秋·山東淄博·高三校考期中）已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，求證：SKIPIF1<0.(2)討論函數(shù)SKIPIF1<0的極值；(3)已知SKIPIF1<0，證明SKIPIF1<05．（2023秋·浙江·高三期末）已知函數(shù)SKIPIF1<0．(1)證明：函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有2個(gè)零點(diǎn)；(2)若函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)：SKIPIF1<0，且SKIPIF1<0．求證：SKIPIF1<0（其中SKIPIF1<0為自然對(duì)數(shù)的底數(shù)）.6．（2023秋·江蘇無(wú)錫·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0，其中a為實(shí)數(shù)．(1)若SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，求a的取值范圍；(2)若SKIPIF1<0，試判斷關(guān)于x的方程SKIPIF1<0在區(qū)間SKIPIF1<0上解的個(gè)數(shù)，并給出證明．（參考數(shù)據(jù)：SKIPIF1<0）7．（2023秋·江蘇蘇州·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0時(shí)，SKIPIF1<0，求實(shí)數(shù)a的取值范圍；(2)討論SKIPIF1<0的零點(diǎn)個(gè)數(shù)．8．（2022秋·江蘇常州·高三?？茧A段練習(xí)）已知SKIPIF1<0，函數(shù)SKIPIF1<0，SKIPIF1<0．(1)討論SKIPIF1<0的單調(diào)性；(2)過(guò)原點(diǎn)分別作曲線SKIPIF1<0和SKIPIF1<0的切線SKIPIF1<0和SKIPIF1<0，試問(wèn)：是否存在SKIPIF1<0，使得切線SKIPIF1<0和SKIPIF1<0的斜率互為倒數(shù)？請(qǐng)說(shuō)明理由；(3)若SKIPIF1<0時(shí)，SKIPIF1<0恒成立，求a的取值范圍．9．（2023春·江蘇南通·高三?？奸_(kāi)學(xué)考試）已知函數(shù)SKIPIF1<0(a≠0)．(1)討論函數(shù)f(x)的單調(diào)性；(2)若a＝1，證明：曲線y＝f(x)與直線y＝x＋1恰有兩個(gè)公共點(diǎn)，且這兩個(gè)公共點(diǎn)關(guān)于點(diǎn)(0，1)對(duì)稱．10．（2023春·廣東揭陽(yáng)·高三?？茧A段練習(xí)）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<0.11．（2023·廣東梅州·統(tǒng)考一模）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SKIPIF1<0，討論函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù).12．（2023·廣東茂名·統(tǒng)考一模）若函數(shù)SKIPIF1<0有兩個(gè)零點(diǎn)SKIPIF1<0，且SKIPIF1<0.(1)求a的取值范圍；(2)若SKIPIF1<0在SKIPIF1<0和SKIPIF1<0處的切線交于點(diǎn)SKIPIF1<0，求證：SKIPIF1<0.13．（2023·湖南邵陽(yáng)·統(tǒng)考二模）已知函數(shù)SKIPIF1<0，SKIPIF1<0．(1)對(duì)任意的SKIPIF1<0，SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍；(2)設(shè)方程SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)的根從小到大依次為SKIPIF1<0，SKIPIF1<0，…，SKIPIF1<0，…，求證：SKIPIF1<0．14．（2023春·湖南長(zhǎng)沙·高三雅禮中學(xué)校考階段練習(xí)）已知函數(shù)SKIPIF1<0，SKIPIF1<0.(1)已知SKIPIF1<0，若SKIPIF1<0時(shí)，SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍；(2)當(dāng)SKIPIF1<0時(shí)，求證：SKIPIF1<0.15．（2023·湖南·湖南師大附中校聯(lián)考模擬預(yù)測(cè)）已知SKIPIF1<0.(1)判斷函數(shù)SKIPIF1<0的單調(diào)性；(2)若SKIPIF1<0是函數(shù)SKIPIF1<0的兩個(gè)極值點(diǎn)，且SKIPIF1<0，求證：SKIPIF1<0.16．（2023春·湖北·高三校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0恒成立，求SKIPIF1<0的最小值；(2)若關(guān)于SKIPIF1<0的方程SKIPIF1<0的兩個(gè)根分別為SKIPIF1<0，證明：SKIPIF1<0.17．（2023春·湖北·高三統(tǒng)考階段練習(xí)）已知SKIPIF1<0.(1)討論SKIPIF1<0的單調(diào)性；(2)若SKIPIF1<0，對(duì)SKIPIF1<0，方程SKIPIF1<0只有唯一實(shí)數(shù)根，求SKIPIF1<0的取值范圍.18．（2023·山東濟(jì)寧·統(tǒng)考一模）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)當(dāng)SKIPIF1<0時(shí)，討論函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù).19．（2023·福建泉州·統(tǒng)考三模）已知SKIPIF1<0有兩個(gè)極值點(diǎn)SKIPIF1<0、SKIPIF1<0，且SKIPIF1<0．(1)求SKIPIF1<0的范圍；(2)當(dāng)SKIPIF1<0時(shí)，證明：SKIPIF1<0．20．（2023春·河北·高三校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0.(1)證明：函數(shù)SKIPIF1<0存在兩個(gè)極值點(diǎn)SKIPIF1<0，且有SKIPIF1<0；(2)試比較函數(shù)SKIPIF1<0的極大值與極小值之和與3的大小，并說(shuō)明理由.21．（2023·江蘇南通·統(tǒng)考模擬預(yù)測(cè)）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<0.22．（2023·浙江嘉興·統(tǒng)考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0，SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)性；(2)若函數(shù)SKIPIF1<0有三個(gè)零點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，求證：SKIPIF1<0.23．（2023·江蘇泰州·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<0.24．（2022秋·浙江紹興·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的取值范圍.(2)求證：SKIPIF1<0.25．（2023秋·浙江紹興·高三統(tǒng)考期末）已知函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，求SKIPIF1<0的取值范圍；(2)函數(shù)SKIPIF1<0有兩個(gè)不同的極值點(diǎn)SKIPIF1<0（其中SKIPIF1<0），證明：SKIPIF1<0；(3)求證：SKIPIF1<0.26．（2023·浙江·校聯(lián)考模擬預(yù)測(cè)）已知SKIPIF1<0，函數(shù)SKIPIF1<0，SKIPIF1<0.(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間和極值；(2)設(shè)SKIPIF1<0較小的零點(diǎn)為SKIPIF1<0，證明：SKIPIF1<0.27．（2023·湖北·統(tǒng)考模擬預(yù)測(cè)）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SKIPIF1<0有3個(gè)零點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，其中SKIPIF1<0．（?。┣髮?shí)數(shù)a的取值范圍；（ⅱ）求證：SKIPIF1<0．28．（2023·福建福州·統(tǒng)考二模）已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0，試判斷SKI