高考數(shù)學(xué)二輪復(fù)習(xí)壓軸題專題03 一元函數(shù)的導(dǎo)數(shù)及其應(yīng)用（利用導(dǎo)函數(shù)研究切線單調(diào)性問題）（選填壓軸題）（原卷版）

專題03一元函數(shù)的導(dǎo)數(shù)及其應(yīng)用（利用導(dǎo)函數(shù)研究切線，單調(diào)性問題）（選填壓軸題）目錄TOC\o"1-2"\h\u一、切線問題 1①已知切線幾條求參數(shù) 1②公切線問題 2③和切線有關(guān)的其它綜合問題 3二、單調(diào)性問題 3①已知單調(diào)區(qū)間求參數(shù) 3②由函數(shù)存在單調(diào)區(qū)間求參數(shù) 4③已知函數(shù)在某區(qū)間上不單調(diào)求參數(shù) 5④利用函數(shù)的單調(diào)性比大小 5一、切線問題①已知切線幾條求參數(shù)1．（2023·全國·高二專題練習(xí)）過坐標原點可以作曲線SKIPIF1<0兩條切線，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023·陜西寶雞·統(tǒng)考二模）若過點SKIPIF1<0可作曲線SKIPIF1<0的三條切線，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023春·廣東深圳·高二統(tǒng)考期末）已知點SKIPIF1<0在直線SKIPIF1<0上運動，若過點SKIPIF1<0恰有三條不同的直線與曲線SKIPIF1<0相切，則點SKIPIF1<0的軌跡長度為（

）A．2 B．4 C．6 D．84．（2023春·廣東佛山·高二校聯(lián)考階段練習(xí)）已知SKIPIF1<0只有一條過原點的切線，則SKIPIF1<0．5．（2023春·四川·高二統(tǒng)考期末）已知函數(shù)SKIPIF1<0，若過點SKIPIF1<0可作曲線SKIPIF1<0的三條切線，則SKIPIF1<0的取值范圍是．6．（2023·全國·高二專題練習(xí)）若曲線SKIPIF1<0有三條經(jīng)過點SKIPIF1<0的切線，則SKIPIF1<0的范圍為．②公切線問題1．（2023·黑龍江哈爾濱·哈爾濱三中?？寄M預(yù)測）已知函數(shù)SKIPIF1<0，SKIPIF1<0，若直線SKIPIF1<0為SKIPIF1<0和SKIPIF1<0的公切線，則b等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023春·河北保定·高二河北省唐縣第一中學(xué)校考階段練習(xí)）若曲線SKIPIF1<0與SKIPIF1<0有三條公切線，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023春·湖北·高二武漢市第四十九中學(xué)校聯(lián)考期中）若直線SKIPIF1<0是曲線SKIPIF1<0與曲線SKIPIF1<0的公切線，則SKIPIF1<0（

）．A．26 B．23 C．15 D．114．（2023春·遼寧鞍山·高二東北育才學(xué)校校聯(lián)考期末）已知函數(shù)SKIPIF1<0，SKIPIF1<0，若曲線SKIPIF1<0與曲線SKIPIF1<0存在公切線，則實數(shù)m的最大值為.5．（2023春·安徽六安·高二六安二中校聯(lián)考期中）設(shè)直線l是函數(shù)SKIPIF1<0，SKIPIF1<0和函數(shù)SKIPIF1<0的公切線，則l的方程是．6．（2023春·江蘇蘇州·高二校聯(lián)考期中）已知函數(shù)SKIPIF1<0.若曲線SKIPIF1<0與曲線SKIPIF1<0有公切線，則實數(shù)m的取值范圍為.③和切線有關(guān)的其它綜合問題1．（2023春·江西吉安·高二統(tǒng)考期末）若動點SKIPIF1<0在曲線SKIPIF1<0上，則動點SKIPIF1<0到直線SKIPIF1<0的距離的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023·全國·高三專題練習(xí)）已知實數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．8 C．4 D．163．（2023·全國·高三專題練習(xí)）若x、a、b為任意實數(shù)，若SKIPIF1<0，則SKIPIF1<0最小值為(

)A．SKIPIF1<0 B．9 C．SKIPIF1<0 D．SKIPIF1<04．（2023·全國·高三專題練習(xí)）已知SKIPIF1<0，SKIPIF1<0，記SKIPIF1<0，則SKIPIF1<0的最小值為．5．（2023春·江蘇南京·高二南京航空航天大學(xué)附屬高級中學(xué)?？计谥校┤鬝KIPIF1<0，則SKIPIF1<0的最小值為.二、單調(diào)性問題①已知單調(diào)區(qū)間求參數(shù)1．（2023春·廣西南寧·高二賓陽中學(xué)校聯(lián)考期末）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023春·吉林松原·高二長春市九臺區(qū)第一中學(xué)校聯(lián)考期末）已知函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023春·河南周口·高二校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，則實數(shù)a的取值范圍是．4．（2023春·高二課時練習(xí)）已知函數(shù)SKIPIF1<0是區(qū)間SKIPIF1<0上的單調(diào)函數(shù)，則SKIPIF1<0的取值范圍是．5．（2023春·高二單元測試）設(shè)函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是減函數(shù)，則SKIPIF1<0的取值范圍是．②由函數(shù)存在單調(diào)區(qū)間求參數(shù)1．（2023春·四川眉山·高二統(tǒng)考期末）若SKIPIF1<0在SKIPIF1<0上存在單調(diào)遞增區(qū)間，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023春·河北邯鄲·高二校聯(lián)考期中）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)存在單調(diào)遞增區(qū)間，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023春·山東泰安·高二統(tǒng)考期末）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在單調(diào)減區(qū)間，則實數(shù)m的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2023春·江西撫州·高二江西省臨川第二中學(xué)?？茧A段練習(xí)）函數(shù)SKIPIF1<0在SKIPIF1<0上存在單調(diào)遞增區(qū)間，則SKIPIF1<0的取值范圍是.5．（2023春·廣西·高二校聯(lián)考期中）若函數(shù)SKIPIF1<0在SKIPIF1<0存在單調(diào)遞減區(qū)間，則a的取值范圍為．6．（2023·全國·高二專題練習(xí)）若函數(shù)SKIPIF1<0存在增區(qū)間，則實數(shù)SKIPIF1<0的取值范圍為.③已知函數(shù)在某區(qū)間上不單調(diào)求參數(shù)1．（2023春·湖南湘潭·高二湘潭縣一中校聯(lián)考期末）已知函數(shù)SKIPIF1<0在SKIPIF1<0上不單調(diào)，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023春·湖南岳陽·高二湖南省岳陽縣第一中學(xué)校考期末）已知函數(shù)SKIPIF1<0在SKIPIF1<0上不是單調(diào)函數(shù)，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023春·四川自貢·高二統(tǒng)考期末）若函數(shù)SKIPIF1<0在其定義域的一個子區(qū)間SKIPIF1<0內(nèi)不是單調(diào)函數(shù)，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023春·上海松江·高二上海市松江一中?？计谀┖瘮?shù)SKIPIF1<0在SKIPIF1<0上不單調(diào)，則實數(shù)k的取值范圍是.5．（2023春·陜西西安·高二統(tǒng)考期末）若函數(shù)SKIPIF1<0在SKIPIF1<0上不單調(diào)，則實數(shù)SKIPIF1<0的取值范圍為.6．（2023春·上海楊浦·高二復(fù)旦附中?？计谥校┮阎瘮?shù)SKIPIF1<0在定義域SKIPIF1<0上不單調(diào)，則正整數(shù)SKIPIF1<0的最小值是.④利用函數(shù)的單調(diào)性比大小1．（2023·江蘇徐州·校考模擬預(yù)測）已知SKIPI