新高考數(shù)學一輪復(fù)習 導(dǎo)數(shù)專項重點難點突破專題14 利用導(dǎo)數(shù)研究函數(shù)零點問題(原卷版)

專題14利用導(dǎo)數(shù)研究函數(shù)零點問題一．函數(shù)零點問題的常見題型：判斷函數(shù)是否存在零點或者求零點的個數(shù)；根據(jù)含參函數(shù)零點情況，求參數(shù)的值或取值范圍.求解步驟：第一步：將問題轉(zhuǎn)化為函數(shù)的零點問題，進而轉(zhuǎn)化為函數(shù)的圖像與SKIPIF1<0軸(或直線SKIPIF1<0)在某區(qū)間上的交點問題；第二步：利用導(dǎo)數(shù)研究該函數(shù)在此區(qū)間上的單調(diào)性、極值、端點值等性質(zhì)，進而畫出其圖像；第三步：結(jié)合圖像判斷零點或根據(jù)零點分析參數(shù).二．利用導(dǎo)數(shù)確定函數(shù)零點的常用方法(1)圖象法：根據(jù)題目要求畫出函數(shù)的圖象，標明函數(shù)極(最)值的位置，借助數(shù)形結(jié)合的思想分析問題（畫草圖時注意有時候需使用極限）．(2)利用函數(shù)零點存在定理：先用該定理判定函數(shù)在某區(qū)間上有零點，然后利用導(dǎo)數(shù)研究函數(shù)的單調(diào)性、極值(最值)及區(qū)間端點值的符號，進而判斷函數(shù)在該區(qū)間上零點的個數(shù)．三．利用函數(shù)的零點求參數(shù)范圍的方法(1)分離參數(shù)(SKIPIF1<0)后，將原問題轉(zhuǎn)化為SKIPIF1<0的值域(最值)問題或轉(zhuǎn)化為直線SKIPIF1<0與SKIPIF1<0的圖象的交點個數(shù)問題(優(yōu)選分離、次選分類)求解；(2)利用函數(shù)零點存在定理構(gòu)建不等式求解；(3)轉(zhuǎn)化為兩個熟悉的函數(shù)圖象的位置關(guān)系問題，從而構(gòu)建不等式求解．專項突破一判斷函數(shù)零點的個數(shù)一、單選題1．函數(shù)SKIPIF1<0所有零點的個數(shù)為（

）A．1 B．2 C．3 D．42．已知函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的零點個數(shù)為（

）A．1 B．0 C．3 D．23．函數(shù)SKIPIF1<0的零點個數(shù)為(

)A．0 B．1 C．2 D．34．已知SKIPIF1<0，則函數(shù)SKIPIF1<0的零點個數(shù)為（

）A．0 B．1 C．2 D．35．已知a∈R，則函數(shù)SKIPIF1<0零點的個數(shù)為（

）A．1 B．2 C．3 D．與a有關(guān)6．已知SKIPIF1<0為R上的可導(dǎo)函數(shù)，當SKIPIF1<0時，SKIPIF1<0，若SKIPIF1<0，則函數(shù)SKIPIF1<0的零點個數(shù)為（

）A．0 B．1 C．2 D．0或2二、填空題7．設(shè)函數(shù)SKIPIF1<0滿足SKIPIF1<0，則函數(shù)SKIPIF1<0的零點個數(shù)為______.8．已知函數(shù)SKIPIF1<0則函數(shù)SKIPIF1<0零點的個數(shù)為___________三、解答題9．已知函數(shù)SKIPIF1<0.(1)求曲線y=f（x）在點（0，f（0））處的切線方程；(2)判斷函數(shù)f（x）的零點的個數(shù)，并說明理由.10．設(shè)函數(shù)SKIPIF1<0.（1）討論SKIPIF1<0在定義域上的單調(diào)性；（2）當SKIPIF1<0時，判斷SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上的零點個數(shù)．11．已知函數(shù)SKIPIF1<0，其中SKIPIF1<0．（1）當SKIPIF1<0時，求SKIPIF1<0的極值；（2）當SKIPIF1<0時，求SKIPIF1<0的零點個數(shù)．12．已知函數(shù)SKIPIF1<0,SKIPIF1<0．(1)討論函數(shù)SKIPIF1<0的單調(diào)性；(2)當SKIPIF1<0時,判斷SKIPIF1<0的零點個數(shù)．13．已知SKIPIF1<0(1)當SKIPIF1<0時，求SKIPIF1<0的單調(diào)性；(2)討論SKIPIF1<0的零點個數(shù)．14．已知函數(shù)SKIPIF1<0.(1)當SKIPIF1<0時，求SKIPIF1<0的單調(diào)區(qū)間；(2)當SKIPIF1<0時，討論SKIPIF1<0的零點個數(shù).15．已知函數(shù)SKIPIF1<0(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間.(2)若SKIPIF1<0，求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的零點個數(shù).16．已知函數(shù)SKIPIF1<0．(1)討論SKIPIF1<0的單調(diào)性；(2)討論SKIPIF1<0在SKIPIF1<0上的零點個數(shù)．專項突破二由函數(shù)零點個數(shù)求參數(shù)一、單選題1．若函數(shù)SKIPIF1<0有且只有2個零點，則實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．若函數(shù)SKIPIF1<0有三個不同的零點，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．若關(guān)于SKIPIF1<0的方程SKIPIF1<0有且只有2個零點，則a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．若函數(shù)SKIPIF1<0有兩個零點，則實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．設(shè)函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0有兩個零點，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知函數(shù)SKIPIF1<0有兩個零點，則實數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知函數(shù)SKIPIF1<0有兩個極值點，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知函數(shù)SKIPIF1<0）有三個零點，則實數(shù)a的取值范圍是（

）A．（0，SKIPIF1<0） B．（0，SKIPIF1<0） C．（0，1） D．（0，e）9．函數(shù)SKIPIF1<0有兩個零點，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知SKIPIF1<0恰有三個不同的零點，則實數(shù)a的范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題11．已知SKIPIF1<0（

）A．若SKIPIF1<0，則SKIPIF1<0，使函數(shù)SKIPIF1<0有2個零點B．若SKIPIF1<0，則SKIPIF1<0，使函數(shù)SKIPIF1<0有2個零點C．若SKIPIF1<0，則SKIPIF1<0，使函數(shù)SKIPIF1<0有2個零點D．若SKIPIF1<0，則SKIPIF1<0，使函數(shù)SKIPIF1<0有2個零點12．已知函數(shù)SKIPIF1<0有兩個零點SKIPIF1<0、SKIPIF1<0，則下列說法正確的是（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0有3個零點，則實數(shù)a可能的取值有（

）A．3 B．2 C．1 D．014．已知函數(shù)SKIPIF1<0在區(qū)間（1，＋∞）內(nèi)沒有零點，則實數(shù)a的取值可以為（

）A．－1 B．2 C．3 D．415．已知函數(shù)SKIPIF1<0在SKIPIF1<0上有兩個不同的零點，則實數(shù)SKIPIF1<0可能取到的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．1三、填空題16．已知函數(shù)SKIPIF1<0有三個零點，則實數(shù)SKIPIF1<0的取值范圍是___________.17．已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0有四個零點，則實數(shù)a的取值范圍是______________.18．已知函數(shù)SKIPIF1<0有兩個零點，則正實數(shù)SKIPIF1<0的取值范圍為______．19．若函數(shù)SKIPIF1<0不存在零點，則實數(shù)a的取值范圍是______.四、解答題20．已知函數(shù)SKIPIF1<0．(1)求SKIPIF1<0的導(dǎo)函數(shù)；(2)若SKIPIF1<0在SKIPIF1<0上有零點，求SKIPIF1<0的取值范圍．21．已知函數(shù)SKIPIF1<0(1)討論函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)的單調(diào)性；(2)若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)無零點，求SKIPIF1<0的取值范圍．22．已知函數(shù)SKIPIF1<0.(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；(2)若函數(shù)SKIPIF1<0至多有兩個零點，求實數(shù)a的取值范圍.23．已知函數(shù)SKIPIF1<0．（1）討論SKIPIF1<0的單調(diào)性；（2）若SKIPIF1<0存在兩個零點，求實數(shù)SKIPIF1<0的取值范圍．24．已知函數(shù)SKIPIF1<0．（Ⅰ）當SKIPIF1<0時，求SKIPIF1<0的極值；（Ⅱ）若SKIPIF1<0在SKIPIF1<0上有兩個不同的零點，求a的取值范圍．25．已知函數(shù)SKIPIF1<0(1)求函數(shù)SKIPIF1<0的圖象在點SKIPIF1<0處的切線方程；(2)證明：函數(shù)SKIPIF1<0有且僅有兩個零點SKIPIF1<0，且SKIPIF1<026．已知函數(shù)SKIPIF1<0.(1)當SKIPIF1<0時，求SKIPIF1<0的單調(diào)區(qū)