新高考數(shù)學(xué)二輪復(fù)習(xí)解答題培優(yōu)練習(xí)專題01 利用導(dǎo)函數(shù)研究函數(shù)的切線問題(典型題型歸類訓(xùn)練) 原卷版

專題01利用導(dǎo)函數(shù)研究函數(shù)的切線問題(典型題型歸類訓(xùn)練)目錄TOC\o"1-2"\h\u一、必備秘籍 1二、典型題型 3題型一：在型求切線方程 3題型二：過型求切線方程 3題型三：已知切線斜率求參數(shù) 3題型四：確定過一點(diǎn)可以做切線條數(shù) 4題型五：已知切線條數(shù)求參數(shù) 4題型六：距離問題轉(zhuǎn)化為相切問題 5題型七：公切線問題 5三、專項(xiàng)訓(xùn)練 6一、必備秘籍1、切線的斜率：函數(shù)SKIPIF1<0在點(diǎn)SKIPIF1<0處的導(dǎo)數(shù)的幾何意義，就是曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線的斜率SKIPIF1<0，即SKIPIF1<0.2、曲線的切線問題（基礎(chǔ)題）（1）在型求切線方程已知：函數(shù)SKIPIF1<0的解析式.計(jì)算：函數(shù)SKIPIF1<0在SKIPIF1<0或者SKIPIF1<0處的切線方程.步驟：第一步：計(jì)算切點(diǎn)的縱坐標(biāo)SKIPIF1<0（方法：把SKIPIF1<0代入原函數(shù)SKIPIF1<0中），切點(diǎn)SKIPIF1<0.第二步：計(jì)算切線斜率SKIPIF1<0.第三步：計(jì)算切線方程.切線過切點(diǎn)SKIPIF1<0，切線斜率SKIPIF1<0。根據(jù)直線的點(diǎn)斜式方程得到切線方程：SKIPIF1<0.（2）過型求切線方程已知：函數(shù)SKIPIF1<0的解析式.計(jì)算：過點(diǎn)SKIPIF1<0（無論該點(diǎn)是否在SKIPIF1<0上）的切線方程.步驟：第一步：設(shè)切點(diǎn)SKIPIF1<0第二步：計(jì)算切線斜率SKIPIF1<0；計(jì)算切線斜率SKIPIF1<0；第三步：令：SKIPIF1<0，解出SKIPIF1<0，代入SKIPIF1<0求斜率第四步：計(jì)算切線方程.根據(jù)直線的點(diǎn)斜式方程得到切線方程：SKIPIF1<0.3、已知SKIPIF1<0，過點(diǎn)SKIPIF1<0，可作曲線的SKIPIF1<0（SKIPIF1<0）條切線問題第一步：設(shè)切點(diǎn)SKIPIF1<0第二步：計(jì)算切線斜率SKIPIF1<0；第三步：計(jì)算切線方程.根據(jù)直線的點(diǎn)斜式方程得到切線方程：SKIPIF1<0.第四步：將SKIPIF1<0代入切線方程，得：SKIPIF1<0，整理成關(guān)于SKIPIF1<0得分方程；第五步：題意已知能作幾條切線，關(guān)于SKIPIF1<0的方程就有幾個(gè)實(shí)數(shù)解；4、已知SKIPIF1<0和SKIPIF1<0存在SKIPIF1<0（SKIPIF1<0）條公切線問題第一步設(shè)SKIPIF1<0的切點(diǎn)SKIPIF1<0設(shè)SKIPIF1<0的切點(diǎn)SKIPIF1<0求公切線的斜率SKIPIF1<0SKIPIF1<0寫出并整理切線SKIPIF1<0整理得：SKIPIF1<0SKIPIF1<0整理得：SKIPIF1<0聯(lián)立已知條件SKIPIF1<0消去SKIPIF1<0得到關(guān)于SKIPIF1<0的方程，再分類變量，根據(jù)題意公切線條數(shù)求交點(diǎn)個(gè)數(shù)；消去SKIPIF1<0得到關(guān)于SKIPIF1<0的方程再分類變量，根據(jù)題意公切線條數(shù)求交點(diǎn)個(gè)數(shù)；二、典型題型題型一：在型求切線方程1．（2023下·遼寧阜新·高二?？计谀┮阎€SKIPIF1<0在SKIPIF1<0處的切線與直線SKIPIF1<0垂直，則實(shí)數(shù)SKIPIF1<0.2．（2023上·山東德州·高三統(tǒng)考期中）函數(shù)SKIPIF1<0在SKIPIF1<0處的切線方程為．（結(jié)果寫成一般式）3．（2023上·上海閔行·高三?？计谥校┣€SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為．4．（2023·安徽·池州市第一中學(xué)校聯(lián)考模擬預(yù)測）已知函數(shù)SKIPIF1<0（其中SKIPIF1<0）在SKIPIF1<0處的切線為SKIPIF1<0，則直線SKIPIF1<0過定點(diǎn)的坐標(biāo)為.5．（2023·陜西寶雞·校聯(lián)考模擬預(yù)測）已知曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線與曲線SKIPIF1<0相切，則SKIPIF1<0.題型二：過型求切線方程1．（2022·四川廣安·廣安二中校考二模）函數(shù)SKIPIF1<0過點(diǎn)SKIPIF1<0的切線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<02．（2022下·河南洛陽·高二校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0，則曲線SKIPIF1<0過坐標(biāo)原點(diǎn)的切線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023·全國·模擬預(yù)測）過原點(diǎn)與曲線SKIPIF1<0相切的一條切線的方程為.4．（2023下·甘肅天水·高二秦安縣第一中學(xué)校考期中）曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處切線的斜率為SKIPIF1<0，過點(diǎn)SKIPIF1<0的切線方程.5．（2023下·四川綿陽·高二期末）過點(diǎn)SKIPIF1<0作曲線SKIPIF1<0的切線，則切線方程為．題型三：已知切線斜率求參數(shù)1．（2023下·遼寧阜新·高二?？计谀┤糁本€SKIPIF1<0與曲線SKIPIF1<0相切，則實(shí)數(shù)a的值為（

）A．SKIPIF1<0 B．0 C．SKIPIF1<0 D．SKIPIF1<02．（2023上·貴州六盤水·高三校聯(lián)考階段練習(xí)）已知直線SKIPIF1<0與曲線SKIPIF1<0相切，則SKIPIF1<0（

）A．1 B．2 C．SKIPIF1<0 D．SKIPIF1<03．（2023上·遼寧·高三?？茧A段練習(xí)）函數(shù)SKIPIF1<0（SKIPIF1<0、SKIPIF1<0）在點(diǎn)SKIPIF1<0處的切線斜率為SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023上·青海西寧·高三統(tǒng)考開學(xué)考試）已知直線SKIPIF1<0與曲線SKIPIF1<0相切，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023上·天津·高三統(tǒng)考期中）已知函數(shù)SKIPIF1<0，若曲線SKIPIF1<0的一條切線的方程為SKIPIF1<0，則SKIPIF1<0.題型四：確定過一點(diǎn)可以做切線條數(shù)1．（2023上·湖北·高三鄂南高中校聯(lián)考期中）函數(shù)SKIPIF1<0為SKIPIF1<0上的奇函數(shù)，過點(diǎn)SKIPIF1<0作曲線SKIPIF1<0的切線，可作切線條數(shù)為（

）A．1 B．2 C．3 D．不確定2．（2021下·北京·高二?？计谥校┮阎瘮?shù)SKIPIF1<0，則曲線SKIPIF1<0過點(diǎn)SKIPIF1<0的切線有（

）A．0條 B．1條 C．2條 D．3條3．（2021下·湖南·高二校聯(lián)考階段練習(xí)）經(jīng)過點(diǎn)SKIPIF1<0作曲線SKIPIF1<0的切線有（

）A．1條 B．2條 C．3條 D．4條4．（2019上·四川內(nèi)江·高三統(tǒng)考階段練習(xí)）已知曲線SKIPIF1<0，則過點(diǎn)SKIPIF1<0可向SKIPIF1<0引切線，其切線條數(shù)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題型五：已知切線條數(shù)求參數(shù)1．（2023·湖南·校聯(lián)考二模）若經(jīng)過點(diǎn)SKIPIF1<0可以且僅可以作曲線SKIPIF1<0的一條切線，則下列選項(xiàng)正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<02．（2023下·陜西漢中·高二校聯(lián)考期中）過點(diǎn)SKIPIF1<0作曲線SKIPIF1<0切線有且只有兩條，則b的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023·全國·校聯(lián)考二模）若曲線SKIPIF1<0有三條過點(diǎn)SKIPIF1<0的切線，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022上·山西運(yùn)城·高三?？茧A段練習(xí)）若過點(diǎn)SKIPIF1<0可以作曲線SKIPIF1<0的兩條切線，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022上·重慶·高三校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0，若過點(diǎn)SKIPIF1<0能作三條直線與SKIPIF1<0的圖像相切，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題型六：距離問題轉(zhuǎn)化為相切問題1．（2022上·四川成都·高三校聯(lián)考階段練習(xí)）曲線SKIPIF1<0上的點(diǎn)到直線SKIPIF1<0的距離的最小值為（

）A．SKIPIF1<0 B．2 C．SKIPIF1<0 D．42．（2023上·湖南長沙·高三長郡中學(xué)?？茧A段練習(xí)）若實(shí)數(shù)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最小值是（

）A．8 B．9 C．10 D．113．（2023下·廣西河池·高二校聯(lián)考期中）若點(diǎn)P是曲線SKIPIF1<0上任意一點(diǎn)，則點(diǎn)P到直線SKIPIF1<0的最小距離為（

）A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．SKIPIF1<0題型七：公切線問題1．（2023上·湖北荊州·高三荊州中學(xué)?？茧A段練習(xí)）若曲線SKIPIF1<0與曲線SKIPIF1<0有公切線，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023·全國·模擬預(yù)測）試寫出曲線SKIPIF1<0與曲線SKIPIF1<0的一條公切線方程.3．（湖北省武漢市部分學(xué)校2023-2024學(xué)年高三上學(xué)期11月調(diào)研考試數(shù)學(xué)試題）寫出曲線SKIPIF1<0與SKIPIF1<0的一條公切線方程：.4．（2023·全國·高三專題練習(xí)）若兩曲線SKIPIF1<0與SKIPIF1<0存在公切線，則正實(shí)數(shù)a的取值范圍是．5．（2023上·重慶·高三重慶巴蜀中學(xué)?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0(1)當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的極值；(2)若曲線SKIPIF1<0與曲線SKIPIF1<0存在2條公切線，求a的取值范圍.三、專項(xiàng)訓(xùn)練1．（2024上·廣東廣州·高三統(tǒng)考階段練習(xí)）已知曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線的傾斜角為SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．-2 D．SKIPIF1<02．（2024上·內(nèi)蒙古赤峰·高三統(tǒng)考開學(xué)考試）函數(shù)SKIPIF1<0的圖象在點(diǎn)SKIPIF1<0處的切線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023下·高二課時(shí)練習(xí)）若曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0不存在4．（2023上·江蘇·高三江蘇省白蒲高級中學(xué)校聯(lián)考階段練習(xí)）若直線SKIPIF1<0是曲線SKIPIF1<0的一條切線，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0ln2 D．SKIPIF1<05．（2023·全國·模擬預(yù)測）已知函數(shù)SKIPIF1<0，過點(diǎn)SKIPIF1<0可作曲線SKIPIF1<0的切線條數(shù)為（

）A．1 B．2 C．3 D．46．（2023·海南·校聯(lián)考模擬預(yù)測）已知函數(shù)SKIPIF1<0，過點(diǎn)SKIPIF1<0作曲線SKIPIF1<0的兩條切線，切點(diǎn)分別為SKIPIF1<0和SKIPIF1<0，若SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0（

）A．0 B．1 C．2 D．37．（2023·四川綿陽·統(tǒng)考模擬預(yù)測）若函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0的圖象在公共點(diǎn)處有相同的切線，則實(shí)數(shù)SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2023上·四川·高三校聯(lián)考階段練習(xí)）若點(diǎn)SKIPIF1<0是曲線SKIPIF1<0上任意一點(diǎn)，則點(diǎn)SKIPIF1<0到直線SKIPIF1<0距離的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（2023上·四川成都·高三校聯(lián)考階段練習(xí)）過點(diǎn)SKIPIF1<0作曲線SKIPIF1<0的兩條切線，切點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．2二、多選題10．（2023下·高二課時(shí)練習(xí)）若曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程是SKIPIF1<0，則（

）A．SKIPIF1<0