4.1切線方程（精講）（提升版）思維導(dǎo)圖思維導(dǎo)圖考點(diǎn)呈現(xiàn)考點(diǎn)呈現(xiàn)例題剖析例題剖析考點(diǎn)一斜率和傾斜角【例1-1】（2022·江蘇淮安）已知函數(shù)SKIPIF1<0在SKIPIF1<0處的切線斜率為SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例1-2】（2022·重慶一中）已知偶函數(shù)SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0的圖象在點(diǎn)SKIPIF1<0處的切線的斜率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·遼寧）已知曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線與直線SKIPIF1<0垂直，則實(shí)數(shù)a的值為______．2．（2022·湖南·長沙縣第一中學(xué)模擬預(yù)測）函數(shù)SKIPIF1<0的圖象在SKIPIF1<0處的切線對應(yīng)的傾斜角為SKIPIF1<0，則sin2SKIPIF1<0=（

）A．SKIPIF1<0 B．±SKIPIF1<0 C．SKIPIF1<0 D．±SKIPIF1<03．（2022·湖南）已知P是曲線SKIPIF1<0上的一動點(diǎn)，曲線C在P點(diǎn)處的切線的傾斜角為SKIPIF1<0，若SKIPIF1<0，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)二“在型”的切線方程【例2-1】（2022·廣西）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<0【例2-2】（2022·廣西·貴港市）已知曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為SKIPIF1<0，則（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<0【一隅三反】1．（2022·河南）已知函數(shù)SKIPIF1<0的圖象經(jīng)過坐標(biāo)原點(diǎn)，則曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·安徽）已知SKIPIF1<0為奇函數(shù)，且當(dāng)SKIPIF1<0時SKIPIF1<0，則曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·安徽·巢湖市）曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．14．（2022·湖北·武漢二中模擬預(yù)測）已知函數(shù)SKIPIF1<0，直線SKIPIF1<0是曲線SKIPIF1<0的一條切線，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)三“過型”的切線方程【例3】（2022·河南洛陽）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<0【一隅三反】1．（2022·廣東·新會陳經(jīng)綸中學(xué)）（多選）已知曲線SKIPIF1<0.則曲線過點(diǎn)P（1，3）的切線方程為.（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02（2022·北京·匯文中學(xué)）SKIPIF1<0過點(diǎn)SKIPIF1<0的切線方程是__________.3．（2022·四川·廣安二中）函數(shù)SKIPIF1<0過點(diǎn)SKIPIF1<0的切線方程為考點(diǎn)四切線或切點(diǎn)數(shù)量問題【例4-1】（2022·河南洛陽）若過點(diǎn)SKIPIF1<0作曲線SKIPIF1<0的切線，則這樣的切線共有（

）A．0條 B．1條 C．2條 D．3條【例4-2】（2022·全國·高三專題練習(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<0【一隅三反】1．（2022·河南洛陽）若過點(diǎn)SKIPIF1<0作曲線SKIPIF1<0的切線，則這樣的切線共有（

）A．0條 B．1條 C．2條 D．3條2．（2022·湖北·宜城市第一中學(xué)）若過點(diǎn)SKIPIF1<0可以作曲線SKIPIF1<0的兩條切線，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0且SKIPIF1<03．（2022·河南洛陽）若過點(diǎn)SKIPIF1<0可作出曲線SKIPIF1<0的三條切線，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國·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________________．考點(diǎn)五公切線【例5-1】（2022·安徽省舒城中學(xué)）已知直線l是曲線SKIPIF1<0與SKIPIF1<0的公共切線，則l的方程為_____.【例5-2】（2022·江蘇·南京外國語學(xué)校模擬預(yù)測）若兩曲線y=x2-1與y=alnx-1存在公切線，則正實(shí)數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全國·模擬預(yù)測）若直線SKIPIF1<0與曲線SKIPIF1<0和SKIPIF1<0都相切，則SKIPIF1<0的斜率為______．2．（2022·河北保定·二模）（多選）若直線SKIPIF1<0是曲線SKIPIF1<0與曲線SKIPIF1<0的公切線，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·安徽·合肥一六八中學(xué)）若直線SKIPIF1<0是曲線SKIPIF1<0的切線，也是曲線SKIPIF1<0的切線，則SKIPIF1<0__________.考點(diǎn)六切線與其他知識的運(yùn)用【例6-1】（2022·湖北·黃岡中學(xué)）已知a，b為正實(shí)數(shù)，直線SKIPIF1<0與曲線SKIPIF1<0相切，則SKIPIF1<0的最小值為（

）A．8 B．9 C．10 D．13【例6-2】（2022·廣東·深圳市光明區(qū)高級中學(xué)）已知函數(shù)SKIPIF1<0，則曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線SKIPIF1<0恒過定點(diǎn)_____________.【一隅三反】1．（2022·河北衡水）已知函數(shù)SKIPIF1<0在SKIPIF1<0處的切線為l，第一象限內(nèi)的點(diǎn)SKIPIF1<0在切線l上，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·安徽）對于三次函數(shù)SKIPIF1<0，若曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線與曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處點(diǎn)的切線重合，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·黑龍江·哈爾濱三中）若曲線SKIPIF1<0過點(diǎn)SKIPIF1<0的切線恒在函數(shù)SKIPIF1<0的圖象的上方，則實(shí)數(shù)a的取值范圍是__________．考點(diǎn)七切線方程的運(yùn)用【例7-1】（2022·全國·高三專題練習(xí)）設(shè)點(diǎn)P在曲線SKIPIF1<0上，點(diǎn)Q在曲線SKIPIF1<0上，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例7-2】（2022·山東煙臺·三模）已知函數(shù)SKIPIF1<0，若方程SKIPIF1<0有且僅有三個實(shí)數(shù)解，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·江蘇徐州）過平面內(nèi)一點(diǎn)P作曲線SKIPIF1<0的兩條互相垂直的切線SKIPIF1<0，切點(diǎn)分別為SKIPIF1<0（SK