新高考數(shù)學(xué)二輪復(fù)習(xí)易錯點04 導(dǎo)數(shù)及其應(yīng)用（原卷版）

易錯點04導(dǎo)數(shù)及其應(yīng)用易錯題【01】不會利用等價轉(zhuǎn)化思想及導(dǎo)數(shù)的幾何意義研究曲線的切線求曲線的切線方程一定要注意區(qū)分“過點A的切線方程”與“在點A處的切線方程”的不同．雖只有一字之差,意義完全不同,“在”說明這點就是切點,“過”只說明切線過這個點,這個點不一定是切點,求曲線過某點的切線方程一般先設(shè)切點把問題轉(zhuǎn)化為在某點處的切線,求過某點的切線條數(shù)一般也是先設(shè)切點,把問題轉(zhuǎn)化為關(guān)于切點橫坐標(biāo)的方程實根個數(shù)問題.易錯題【02】對極值概念理解不準(zhǔn)確致對于可導(dǎo)函數(shù)f(x)：x0是極值點的充要條件是在x0點兩側(cè)導(dǎo)數(shù)異號,即f′(x)在方程f′(x)＝0的根x0的左右的符號：“左正右負(fù)”?f(x)在x0處取極大值；“左負(fù)右正”?f(x)在x0處取極小值,而不僅是f′(x0)＝0.f′(x0)＝0是x0為極值點的必要而不充分條件．對于給出函數(shù)極大(小)值的條件,一定要既考慮f′(x0)＝0,又考慮檢驗“左正右負(fù)”或“左負(fù)右正”,防止產(chǎn)生增根．易錯題【03】研究含有參數(shù)的函數(shù)單調(diào)性分類標(biāo)準(zhǔn)有誤若函數(shù)的單調(diào)性可轉(zhuǎn)化為解不等式SKIPIF1<0求解此類問題,首先根據(jù)a的符號進(jìn)行討論,當(dāng)a的符號確定后,再根據(jù)SKIPIF1<0是否在定義域內(nèi)討論,當(dāng)SKIPIF1<0都在定義域內(nèi)時在根據(jù)SKIPIF1<0的大小進(jìn)行討論.易錯題【04】不會利用隱零點研究函數(shù)的性質(zhì)函數(shù)零點按是否可求精確解可以分為兩類：一類是數(shù)值上能精確求解的,稱之為“顯零點”；另一類是能夠判斷其存在但無法直接表示的,稱之為“隱零點”.利用導(dǎo)數(shù)求函數(shù)的最值或單調(diào)區(qū)間,常常會把最值問題轉(zhuǎn)化為求導(dǎo)函數(shù)的零點問題,若導(dǎo)數(shù)零點存在,但無法求出,我們可以設(shè)其為SKIPIF1<0,再利用導(dǎo)函數(shù)的單調(diào)性確定SKIPIF1<0所在區(qū)間,最后根據(jù)SKIPIF1<0,研究SKIPIF1<0,我們把這類問題稱為隱零點問題.注意若SKIPIF1<0中含有參數(shù)a,關(guān)系式SKIPIF1<0是關(guān)于SKIPIF1<0的關(guān)系式,確定SKIPIF1<0的合適范圍,往往和SKIPIF1<0的范圍有關(guān). 01(2022新高考1卷T7)若過點SKIPIF1<0可以作曲線SKIPIF1<0的兩條切線,則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<01.(2021屆陜西西安中學(xué)高三期中)若函數(shù)SKIPIF1<0存在平行于SKIPIF1<0軸的切線,則實數(shù)SKIPIF1<0取值范圍是()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02.(2021屆江蘇蘇州市高三月考)若過點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 02已知f(x)＝x3＋ax2＋bx＋a2在x＝1處有極值為10,則a＋b＝________.(2022全國1卷T12)設(shè)SKIPIF1<0,若SKIPIF1<0為函數(shù)SKIPIF1<0的極大值點,則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．(2021屆山西長治市高三月考)已知函數(shù)SKIPIF1<0在SKIPIF1<0處取得極值0,則SKIPIF1<0()A．2 B．7 C．2或7 D．3或9 03(2021新高考2卷T22(1))已知函數(shù)SKIPIF1<0．(1)討論SKIPIF1<0的單調(diào)性；1.(2021屆河南高三月考)已知函數(shù)SKIPIF1<0SKIPIF1<0(1)已知點SKIPIF1<0為曲線SKIPIF1<0上一點,若該曲線在點SKIPIF1<0處的切線方程為SKIPIF1<0(SKIPIF1<0,SKIPIF1<0),求SKIPIF1<0,SKIPIF1<0,SKIPIF1<0的值；(2)討論函數(shù)SKIPIF1<0的單調(diào)性；(3)若SKIPIF1<0在區(qū)間SKIPIF1<0上有唯一的極值點SKIPIF1<0,求SKIPIF1<0的取值范圍.2.(2021屆天津市第二十一中學(xué)高三期中)已知函數(shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時,求函數(shù)SKIPIF1<0的單調(diào)區(qū)間和極值；(2)討論函數(shù)SKIPIF1<0單調(diào)性． 04(2021屆福建省龍巖高三月考)已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0為SKIPIF1<0的極值點,求實數(shù)SKIPIF1<0；(2)若SKIPIF1<0在SKIPIF1<0上恒成立,求實數(shù)SKIPIF1<0的范圍.1.(2021屆內(nèi)蒙古海拉爾高三期中)已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0是SKIPIF1<0的極值點,求SKIPIF1<0的單調(diào)區(qū)間；(2)若SKIPIF1<0,求證：SKIPIF1<02.已知SKIPIF1<0,函數(shù)SKIPIF1<0.(1)證明：SKIPIF1<0在SKIPIF1<0上有唯一的極值點；(2)當(dāng)SKIPIF1<0時,求SKIPIF1<0在SKIPIF1<0上的零點個數(shù).錯1．若點SKIPIF1<0不在函數(shù)SKIPIF1<0的圖象上,且過點SKIPIF1<0僅能作一條直線與SKIPIF1<0的圖象相切,則SKIPIF1<0的取值范圍為()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．(2021屆安徽六安市高三月考)函數(shù)SKIPIF1<0存在與直線SKIPIF1<0平行的切線,則實數(shù)SKIPIF1<0的取值范圍是()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．(2021屆遼寧沈陽市高三月考)若直線SKIPIF1<0與曲線SKIPIF1<0相切,則()A．SKIPIF1<0為定值 B．SKIPIF1<0為定值C．SKIPIF1<0為定值 D．SKIPIF1<0為定值4．(2021屆云南高三月考)已知SKIPIF1<0為函數(shù)SKIPIF1<0的極小值點,則SKIPIF1<0()A．1 B．2 C．3 D．SKIPIF1<05．(2021屆河南南陽高三期中)已知函數(shù)SKIPIF1<0在SKIPIF1<0處取得極小值SKIPIF1<0,若SKIPIF1<0,SKIPIF1<0,使得SKIPIF1<0,且SKIPIF1<0,則SKIPIF1<0的最大值為()A．2 B．3 C．4 D．66．(2021山西太原高三期中)若SKIPIF1<0是函數(shù)SKIPIF1<0的極值點,則函數(shù)()A．有最小值SKIPIF1<0,無最大值 B．有最大值SKIPIF1<0,無最小值C．有最小值SKIPIF1<0,最大值SKIPIF1<0 D．無最大值,無最小值7．(2021北京四中高三期中)設(shè)函數(shù)SKIPIF1<0,其中SKIPIF1<0.(1)若SKIPIF1<0是函數(shù)SKIPIF1<0的極值點,求a的值；(2)當(dāng)SKIPIF1<0時,求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；(3)當(dāng)SKIPIF1<0時,設(shè)函數(shù)SKIPIF1<0,證明：SKIPIF1<0.8．(2021河南南陽高三期中)已知函數(shù)SKIPIF1<0,SKIPIF1<0.(