新高考數(shù)學二輪復習分層訓練專題11 導數(shù)在不等式.恒等式和零點問題綜合應用（原卷版）

答案第=page11頁，共=sectionpages22頁專題11導數(shù)在不等式.恒等式和零點問題綜合應用【練基礎(chǔ)】一、單選題1．（2023·陜西咸陽·?？寄M預測）已知SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023·江西·校聯(lián)考一模）已知關(guān)于SKIPIF1<0的不等式SKIPIF1<0對任意SKIPIF1<0恒成立，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．SKIPIF1<03．（2022秋·甘肅武威·高三校考階段練習）函數(shù)SKIPIF1<0的圖像大致是（

）A． B． C． D．4．（2022秋·山東東營·高三廣饒一中?？茧A段練習）設(shè)SKIPIF1<0，若函數(shù)SKIPIF1<0有且只有三個零點，則實數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·江蘇南京·模擬預測）已知函數(shù)SKIPIF1<0（SKIPIF1<0），且SKIPIF1<0在SKIPIF1<0有兩個零點，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022秋·湖南岳陽·高三?？茧A段練習）已知函數(shù)SKIPIF1<0，若方程SKIPIF1<0恰好有三個不等的實數(shù)根，則實數(shù)k的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．（2022·四川遂寧·射洪中學校考模擬預測）已知函數(shù)SKIPIF1<0（其中SKIPIF1<0，SKIPIF1<0）有兩個零點，則a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022秋·河南·高三校聯(lián)考階段練習）已知函數(shù)SKIPIF1<0，則方程SKIPIF1<0在區(qū)間SKIPIF1<0上的實根個數(shù)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．（2023·安徽馬鞍山·統(tǒng)考一模）已知函數(shù)SKIPIF1<0，若SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的可能的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2023·全國·高三專題練習）已知函數(shù)SKIPIF1<0，SKIPIF1<0，則下列說法正確的是（

）A．SKIPIF1<0在SKIPIF1<0上是增函數(shù)B．SKIPIF1<0，不等式SKIPIF1<0恒成立，則正實數(shù)SKIPIF1<0的最小值為SKIPIF1<0C．若SKIPIF1<0有兩個零點SKIPIF1<0，則SKIPIF1<0D．若SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最大值為SKIPIF1<011．（2022·云南昆明·昆明一中?？寄M預測）已知函數(shù)SKIPIF1<0，則（

）A．函數(shù)SKIPIF1<0在SKIPIF1<0處取得最大值B．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減C．函數(shù)SKIPIF1<0有兩個不同的零點D．SKIPIF1<0恒成立12．（2022·全國·校聯(lián)考模擬預測）對于三次函數(shù)SKIPIF1<0，給出定義：設(shè)SKIPIF1<0是函數(shù)SKIPIF1<0的導數(shù)，SKIPIF1<0是函數(shù)SKIPIF1<0的導數(shù)，若方程SKIPIF1<0有實數(shù)解SKIPIF1<0，則稱SKIPIF1<0為函數(shù)SKIPIF1<0的“拐點”.某同學經(jīng)過探究發(fā)現(xiàn)：任何一個三次函數(shù)都有“拐點”；任何一個三次函數(shù)都有對稱中心，且“拐點”就是對稱中心.若函數(shù)SKIPIF1<0，則下列說法正確的是（

）A．SKIPIF1<0的極大值點為SKIPIF1<0B．SKIPIF1<0有且僅有3個零點C．點SKIPIF1<0是SKIPIF1<0的對稱中心D．SKIPIF1<0三、填空題13．（2023·四川瀘州·瀘州老窖天府中學?？寄M預測）已知不等式SKIPIF1<0對SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的最小值為__________.14．（2022·上海奉賢·統(tǒng)考一模）已知某商品的成本SKIPIF1<0和產(chǎn)量SKIPIF1<0滿足關(guān)系SKIPIF1<0，該商品的銷售單價SKIPIF1<0和產(chǎn)量SKIPIF1<0滿足關(guān)系式SKIPIF1<0，則當產(chǎn)量SKIPIF1<0等于__________時，利潤最大.15．（2022·上海普陀·統(tǒng)考一模）設(shè)SKIPIF1<0、SKIPIF1<0、SKIPIF1<0均為正數(shù)且SKIPIF1<0，則使得不等式SKIPIF1<0總成立的SKIPIF1<0的取值范圍為______．16．（2023·全國·高三專題練習）給出定義：設(shè)SKIPIF1<0是函數(shù)SKIPIF1<0的導函數(shù)，SKIPIF1<0是函數(shù)SKIPIF1<0的導函數(shù)，若方程SKIPIF1<0有實數(shù)解SKIPIF1<0，則稱SKIPIF1<0為函數(shù)SKIPIF1<0的“拐點”，經(jīng)研究發(fā)現(xiàn)所有的三次函數(shù)SKIPIF1<0都有“拐點”，且該“拐點”也是函數(shù)SKIPIF1<0的圖像的對稱中心，若函數(shù)SKIPIF1<0，則SKIPIF1<0______.四、解答題17．（2023·浙江·永嘉中學校聯(lián)考模擬預測）已知SKIPIF1<0為正實數(shù)，函數(shù)SKIPIF1<0.(1)若SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍；(2)求證：SKIPIF1<0（SKIPIF1<0）.18．（2023·全國·唐山市第十一中學?？寄M預測）已知SKIPIF1<0為正整數(shù)，SKIPIF1<0，SKIPIF1<0.(1)求SKIPIF1<0的最大值；(2)若SKIPIF1<0恒成立，求正整數(shù)SKIPIF1<0的取值的集合.（參考數(shù)據(jù)：SKIPIF1<0）19．（2023·廣東惠州·統(tǒng)考模擬預測）已知函數(shù)SKIPIF1<0．(1)當SKIPIF1<0時，求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；(2)若函數(shù)SKIPIF1<0恒成立，求實數(shù)a的取值范圍．20．（2023·四川涼山·統(tǒng)考一模）已知函數(shù)SKIPIF1<0．(1)求SKIPIF1<0的最小值；(2)已知SKIPIF1<0，證明：SKIPIF1<0；(3)若SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍．【提能力】一、單選題21．（2022秋·山西陽泉·高三陽泉市第一中學校?？计谥校┰O(shè)函數(shù)SKIPIF1<0，其中SKIPIF1<0，若存在唯一的整數(shù)SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<022．（2023·全國·高三專題練習）SKIPIF1<0，則a，b，c的大小順序為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<023．（2022·全國·高三專題練習）已知函數(shù)SKIPIF1<0只有一個零點，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<024．（2023·全國·高三專題練習）已知SKIPIF1<0，設(shè)函數(shù)SKIPIF1<0若關(guān)于SKIPIF1<0的不等式SKIPIF1<0在SKIPIF1<0上恒成立，則SKIPIF1<0的取值范圍為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<025．（2023·全國·高三對口高考）函數(shù)SKIPIF1<0在SKIPIF1<0的圖象大致為（

）A． B．C． D．26．（2023·全國·高三專題練習）已知函數(shù)SKIPIF1<0在SKIPIF1<0上有零點，則m的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<027．（2022·全國·高三專題練習）已知函數(shù)SKIPIF1<0若關(guān)于SKIPIF1<0的不等式SKIPIF1<0在SKIPIF1<0上恒成立，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<028．（2022·全國·高三專題練習）已知函數(shù)SKIPIF1<0若函數(shù)SKIPIF1<0恰有5個零點，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<029．（2023·四川綿陽·四川省綿陽南山中學?？家荒＃┮阎瘮?shù)SKIPIF1<0有兩個不同的極值點SKIPIF1<0，且不等式SKIPIF1<0恒成立，則實數(shù)t的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題30．（2021·全國·高三專題練習）對于函數(shù)SKIPIF1<0，下列說法正確的有（

）A．SKIPIF1<0在SKIPIF1<0處取得極大值SKIPIF1<0B．SKIPIF1<0有兩不同零點C．SKIPIF1<0D．若SKIPIF1<0在SKIPIF1<0上恒成立，則SKIPIF1<031．（2023秋·山東·高三山東省實驗中學?？茧A段練習）已知函數(shù)SKIPIF1<0，則下列結(jié)論中正確的是（

）A．若SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值與最小值分別為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0B．曲線SKIPIF1<0與直線SKIPIF1<0相切C．若SKIPIF1<0為增函數(shù)，則SKIPIF1<0的取值范圍為SKIPIF1<0D．SKIPIF1<0在SKIPIF1<0上最多有SKIPIF1<0個零點32．（2023·全國·高三專題練習）已知函數(shù)SKIPIF1<0，下列命題正確的是（

）A．若SKIPIF1<0是函數(shù)SKIPIF1<0的極值點，則SKIPIF1<0B．若SKIPIF1<0是函數(shù)SKIPIF1<0的極值點，則SKIPIF1<0在SKIPIF1<0上的最小值為SKIPIF1<0C．若SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則SKIPIF1<0D．若SKIPIF1<0在SKIPIF1<0上恒成立，則SKIPIF1<033．（2023·全國·高三專題練習）若SKIPIF1<0，SKIPIF1<0為自然對數(shù)的底數(shù)，則下列結(jié)論錯誤的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、填空題34．（2022·全國·高三專題練習）設(shè)函數(shù)SKIPIF1<0恰有兩個極值點，則實數(shù)t的取值范圍為___________.35．（2022·全國·高三專題練習）已知不等式SKIPIF1<0對任意SKIPIF1<0恒成立，則實數(shù)a的取值范圍是___________.36．（2021春·全國·高三專題練習）若SKIPIF1<0時，關(guān)于SKIPIF1<0不等式SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的最大值是______.37．（2023·全國·高三專題練習）已知函數(shù)SKIPIF1<0，給出下列四個結(jié)論：①若SKIPIF1<0，SKIPIF1<0恰有2個零點；②存在負數(shù)SKIPIF1<0，使得SKIPIF1<0恰有1個零點；③存在負數(shù)