新高考數(shù)學(xué)二輪復(fù)習(xí)重難點(diǎn)突破專題15 已知函數(shù)的單調(diào)區(qū)間求參數(shù)的范圍(原卷版)

專題15已知函數(shù)的單調(diào)區(qū)間求參數(shù)的范圍一、單選題1．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知函數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0的圖象過定點(diǎn)SKIPIF1<0，對于任意SKIPIF1<0，有SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的范圍為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．函數(shù)SKIPIF1<0是SKIPIF1<0上的單調(diào)函數(shù)，則SKIPIF1<0的范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知函數(shù)SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上為增函數(shù)，在SKIPIF1<0上為減函數(shù)，則實(shí)數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則實(shí)數(shù)a的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．對任意的SKIPIF1<0，都有SKIPIF1<0，則SKIPIF1<0的最大值為（）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．函數(shù)SKIPIF1<0單調(diào)遞增的必要不充分條件有（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．設(shè)函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間是SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知函數(shù)SKIPIF1<0在定義域SKIPIF1<0上的導(dǎo)函數(shù)為SKIPIF1<0，若函數(shù)SKIPIF1<0沒有零點(diǎn)，且SKIPIF1<0SKIPIF1<0，當(dāng)SKIPIF1<0在SKIPIF1<0上與SKIPIF1<0在SKIPIF1<0上的單調(diào)性相同時(shí)，則實(shí)數(shù)k的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．若函數(shù)SKIPIF1<0在SKIPIF1<0上是減函數(shù)，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．已知函數(shù)SKIPIF1<0，若SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0處取得最大值，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．已知函數(shù)SKIPIF1<0，是單調(diào)遞增函數(shù)，則實(shí)數(shù)a的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上不是單調(diào)函數(shù)，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）.A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<017．若函數(shù)SKIPIF1<0在SKIPIF1<0是增函數(shù)，則實(shí)數(shù)a的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、解答題18．已知函數(shù)SKIPIF1<0，SKIPIF1<0.（1）當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0在SKIPIF1<0上的最大值和最小值；（2）若SKIPIF1<0在SKIPIF1<0上單調(diào)，求SKIPIF1<0的取值范圍.19．設(shè)函數(shù)SKIPIF1<0，其中SKIPIF1<0為自然對數(shù)的底數(shù).（1）若SKIPIF1<0在定義域上是增函數(shù)，求SKIPIF1<0的取值范圍；（2）若直線SKIPIF1<0是函數(shù)SKIPIF1<0的切線，求實(shí)數(shù)SKIPIF1<0的值；20．已知a＞0，函數(shù)SKIPIF1<0．（1）若f（x）為減函數(shù)，求實(shí)數(shù)a的取值范圍；（2）當(dāng)x＞1時(shí)，求證：SKIPIF1<0．（e＝2.718…）21．已知函數(shù)SKIPIF1<0，SKIPIF1<0.（1）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)是增函數(shù)，求SKIPIF1<0的取值范圍；（2）證明：SKIPIF1<0.22．已知函數(shù)SKIPIF1<0的圖象過點(diǎn)SKIPIF1<0，且在P處的切線恰好與直線SKIPIF1<0垂直．（1）求SKIPIF1<0的解析式；（2）若SKIPIF1<0在SKIPIF1<0上是減函數(shù)，求m的取值范圍．23．已知SKIPIF1<0，函數(shù)SKIPIF1<0.（1）當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程；（2）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是減函數(shù)，求SKIPIF1<0的取值范圍.24．已知函數(shù)SKIPIF1<0SKIPIF1<0，SKIPIF1<0是偶函數(shù)．（1）求函數(shù)SKIPIF1<0的極值以及對應(yīng)的極值點(diǎn)．（2）若函數(shù)SKIPIF1<0，且SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，求實(shí)數(shù)SKIPIF1<0的取值范圍．25．已知函數(shù)SKIPIF1<0，SKIPIF1<0.（1）若函數(shù)SKIPIF1<0在SKIPIF1<0上存在單調(diào)遞增區(qū)間，求實(shí)數(shù)SKIPIF1<0的取值范圍；（2）設(shè)SKIPIF1<0.若SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上的最小值為SKIPIF1<0，求SKIPIF1<0在SKIPIF1<0上取得最大值時(shí)，對應(yīng)的SKIPIF1<0值.26．已知三次函數(shù)SKIPIF1<0.（1）當(dāng)SKIPIF1<0時(shí)，求曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程；（2）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上具有單調(diào)性，求SKIPIF1<0的取值范圍；（3）當(dāng)SKIPIF1<0時(shí)，若SKIPIF1<0，求SKIPIF1<0的取值范圍.27．設(shè)函數(shù)SKIPIF1<0，其中SKIPIF1<0.（1）若曲線SKIPIF1<0在SKIPIF1<0的切線方程為SKIPIF1<0，求a，b的值；（2）若SKIPIF1<0在SKIPIF1<0處取得極值，求a的值；（3）若SKIPIF1<0在SKIPIF1<0上為增函數(shù)，求a的取值范圍.28．已知函數(shù)SKIPIF1<0，其中SKIPIF1<0.（1）若SKIPIF1<0在SKIPIF1<0內(nèi)為減函數(shù)，求實(shí)數(shù)a的取值范圍；（2）求函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值.29．已知函數(shù)SKIPIF1<0．（1）令SKIPIF1<0，若函數(shù)SKIPIF1<0在其定義域上單調(diào)遞增，求實(shí)數(shù)SKIPIF1<0的取值范圍；（2）求證：SKIPIF1<0．30．已知：函數(shù)SKIPIF1<0.（1）當(dāng)SKIPIF1<0時(shí)，討論函數(shù)SKIPIF1<0的單調(diào)性；（2）若SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，求實(shí)數(shù)SKIPIF1<0的取值范圍.31．已知函數(shù)SKIPIF1<0，（1）當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0的單調(diào)區(qū)間與極值；（2）是否存在正實(shí)數(shù)SKIPIF1<0，使得函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上為減函數(shù)？若存在，請求SKIPIF1<0的取值范圍；若不存在，請說明理由.32．設(shè)函數(shù)SKIPIF1<0（SKIPIF1<0為常數(shù)）．（1）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是單調(diào)遞增函數(shù)，求實(shí)數(shù)SKIPIF1<0的取值范圍；（2）若函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)SKIPIF1<0、SKIPIF1<0，且SKIPIF1<0，求證：SKIPIF1<0．33．已知函數(shù)SKIPIF1<0.（1）若SKIPIF1<0在SKIPIF1<0單調(diào)遞增，求SKIPIF1<0的取值范圍：（2）若SKIPIF1<0，證明：當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0.34．已知函數(shù)SKIPIF1<0（1）若函數(shù)SKIPIF1<0的圖象在SKIPIF1<0處的切線斜率為1，求實(shí)數(shù)SKIPIF1<0的值；并求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；（2）若函數(shù)SKIPIF1<0在SKIPIF1<0上是減函數(shù)，求實(shí)數(shù)SKIPIF1<0的取值范圍.35．已知函數(shù)SKIPIF1<0在SKIPIF1<0的切線與直線SKIPIF1<0垂直，函數(shù)SKIPIF1<0．（1）求實(shí)數(shù)a的值；（2）若函數(shù)SKIPIF1<0存在單調(diào)遞減區(qū)間，求實(shí)數(shù)b的取值范圍；36．設(shè)函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0.（1）若函數(shù)SKIPIF1<0為奇函數(shù)，求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的單調(diào)性；（2）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)不單調(diào)，求實(shí)數(shù)SKIPIF1<0的取值范圍.37．已知函數(shù)SKIPIF1<0（SKIPIF1<0，常