新高考數(shù)學(xué)一輪復(fù)習(xí)講練測第3章第01講 導(dǎo)數(shù)的概念與運(yùn)算（練習(xí)）（原卷版）

第01講導(dǎo)數(shù)的概念與運(yùn)算（模擬精練+真題演練）1．（2023·全國·模擬預(yù)測）已知SKIPIF1<0為實(shí)數(shù)，函數(shù)SKIPIF1<0是偶函數(shù)，則曲線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·陜西寶雞·統(tǒng)考二模）已知拋物線C：SKIPIF1<0，（SKIPIF1<0）的焦點(diǎn)為F，SKIPIF1<0為C上一動點(diǎn)，若曲線C在點(diǎn)M處的切線的斜率為SKIPIF1<0，則直線FM的斜率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023·陜西榆林·統(tǒng)考模擬預(yù)測）已知函數(shù)SKIPIF1<0，若SKIPIF1<0的圖象在SKIPIF1<0處的切線與坐標(biāo)軸圍成的三角形的面積為1，則SKIPIF1<0（

）A．SKIPIF1<0 B．2 C．±2 D．SKIPIF1<04．（2023·浙江紹興·統(tǒng)考模擬預(yù)測）如圖是函數(shù)SKIPIF1<0的導(dǎo)函數(shù)SKIPIF1<0的圖象，若SKIPIF1<0，則SKIPIF1<0的圖象大致為（

）A． B．C． D．5．（2023·山東濰坊·統(tǒng)考模擬預(yù)測）設(shè)SKIPIF1<0為SKIPIF1<0上的可導(dǎo)函數(shù)，且SKIPIF1<0，則曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線斜率為（

）A．2 B．-1 C．1 D．SKIPIF1<06．（2023·河南鄭州·統(tǒng)考模擬預(yù)測）若過原點(diǎn)與曲線SKIPIF1<0相切的直線，切點(diǎn)均與原點(diǎn)不重合的有2條，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023·湖南衡陽·校聯(lián)考模擬預(yù)測）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<08．（2023·湖北·模擬預(yù)測）已知函數(shù)SKIPIF1<0，都有SKIPIF1<0的最小值為0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（多選題）（2023·重慶·校聯(lián)考三模）德國數(shù)學(xué)家萊布尼茨是微積分的創(chuàng)立者之一，他從幾何問題出發(fā)，引進(jìn)微積分概念．在研究切線時(shí)認(rèn)識到，求曲線的切線的斜率依賴于縱坐標(biāo)的差值和橫坐標(biāo)的差值，以及當(dāng)此差值變成無限小時(shí)它們的比值，這也正是導(dǎo)數(shù)的幾何意義．設(shè)SKIPIF1<0是函數(shù)SKIPIF1<0的導(dǎo)函數(shù)，若SKIPIF1<0，對SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，總有SKIPIF1<0，則下列選項(xiàng)正確的是（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<010．（多選題）（2023·黑龍江齊齊哈爾·齊齊哈爾市實(shí)驗(yàn)中學(xué)?？既＃┤粢粭l直線與兩條或兩條以上的曲線均相切，則稱該直線為這些曲線的公切線，已知直線SKIPIF1<0：SKIPIF1<0為曲線SKIPIF1<0：SKIPIF1<0和SKIPIF1<0：SKIPIF1<0的公切線，則下列結(jié)論正確的是（

）A．曲線SKIPIF1<0的圖象在SKIPIF1<0軸的上方B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0和SKIPIF1<0必存在斜率為SKIPIF1<0的公切線11．（多選題）（2023·全國·校聯(lián)考模擬預(yù)測）已知函數(shù)SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與曲線SKIPIF1<0相切，則與直線SKIPIF1<0垂直的直線為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．（多選題）（2023·江蘇南通·模擬預(yù)測）過平面內(nèi)一點(diǎn)P作曲線SKIPIF1<0兩條互相垂直的切線SKIPIF1<0、SKIPIF1<0，切點(diǎn)為SKIPIF1<0、SKIPIF1<0、SKIPIF1<0不重合SKIPIF1<0，設(shè)直線SKIPIF1<0、SKIPIF1<0分別與y軸交于點(diǎn)A、B，則（

）A．SKIPIF1<0、SKIPIF1<0兩點(diǎn)的縱坐標(biāo)之積為定值 B．直線SKIPIF1<0的斜率為定值C．線段AB的長度為定值 D．SKIPIF1<0面積的取值范圍為SKIPIF1<013．（2023·重慶·統(tǒng)考模擬預(yù)測）已知函數(shù)SKIPIF1<0，若這兩個(gè)函數(shù)的圖象在公共點(diǎn)SKIPIF1<0處有相同的切線，則SKIPIF1<0_________．14．（2023·甘肅金昌·永昌縣第一高級中學(xué)統(tǒng)考模擬預(yù)測）曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為______．15．（2023·河北唐山·開灤第二中學(xué)?？寄M預(yù)測）已知函數(shù)SKIPIF1<0的圖象在SKIPIF1<0處的切線與在SKIPIF1<0處的切線相互垂直，則SKIPIF1<0的最小值是___________.16．（2023·湖北武漢·華中師大一附中校考模擬預(yù)測）若函數(shù)SKIPIF1<0的圖象上存在不同的兩點(diǎn)，使函數(shù)圖象在這兩點(diǎn)處的切線斜率之積小于0且斜率之和等于常數(shù)e，則稱該函數(shù)為“e函數(shù)”，下列四個(gè)函數(shù)中，其中為“e函數(shù)”的是________．①SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0；④SKIPIF1<01．（2019·全國·統(tǒng)考高考真題）已知曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為SKIPIF1<0，則A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2019·全國·高考真題）曲線y=2sinx+cosx在點(diǎn)(π，–1)處的切線方程為A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·統(tǒng)考高考真題）曲線SKIPIF1<0過坐標(biāo)原點(diǎn)的兩條切線的方程為____________，____________．4．（2022·全國·統(tǒng)考高考真題）若曲線SKIPIF1<0有兩條過坐標(biāo)原點(diǎn)的切線，則a的取值范圍是________________．5．（2021·全國·統(tǒng)考高考真題）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_______．6．（