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專題14分類討論證明或求函數(shù)的單調(diào)區(qū)間(含參)1.設(shè)函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時(shí),討論SKIPIF1<0在SKIPIF1<0內(nèi)的單調(diào)性;(2)當(dāng)SKIPIF1<0時(shí),證明:SKIPIF1<0有且僅有兩個(gè)零點(diǎn).2.已知函數(shù)SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)區(qū)間;(2)當(dāng)SKIPIF1<0時(shí),求證:SKIPIF1<0.3.已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0,求SKIPIF1<0在區(qū)間SKIPIF1<0上的極值;(2)討論函數(shù)SKIPIF1<0的單調(diào)性.4.已知函數(shù)SKIPIF1<0.(1)試討論SKIPIF1<0的單調(diào)性;(2)若SKIPIF1<0,證明:SKIPIF1<0.5.已知函數(shù)SKIPIF1<0,a為非零常數(shù).(1)求SKIPIF1<0單調(diào)遞減區(qū)間;(2)討論方程SKIPIF1<0的根的個(gè)數(shù).6.已知函數(shù)SKIPIF1<0,SKIPIF1<0.(1)判斷函數(shù)SKIPIF1<0的單調(diào)性;(2)若SKIPIF1<0,判斷是否存在實(shí)數(shù)SKIPIF1<0,使函數(shù)SKIPIF1<0的最小值為2?若存在求出SKIPIF1<0的值;若不存在,請(qǐng)說(shuō)明理由;(3)證明:SKIPIF1<0.7.已知函數(shù)SKIPIF1<0,SKIPIF1<0.(1)判斷函數(shù)SKIPIF1<0的單調(diào)性;(2)若SKIPIF1<0,判斷是否存在實(shí)數(shù)SKIPIF1<0,使函數(shù)SKIPIF1<0的最小值為2?若存在求出SKIPIF1<0的值;若不存在,請(qǐng)說(shuō)明理由;8.已知函數(shù)SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)性.(2)若SKIPIF1<0,設(shè)SKIPIF1<0是函數(shù)SKIPIF1<0的兩個(gè)極值點(diǎn),若SKIPIF1<0,求證:SKIPIF1<0.9.已知函數(shù)SKIPIF1<0.(1)討論SKIPIF1<0的單調(diào)區(qū)間;(2)當(dāng)SKIPIF1<0時(shí),證明:SKIPIF1<0.10.已知函數(shù)SKIPIF1<0.(1)試討論函數(shù)SKIPIF1<0的單調(diào)性;(2)對(duì)任意SKIPIF1<0,滿足SKIPIF1<0的圖象與直線SKIPIF1<0恒有且僅有一個(gè)公共點(diǎn),求k的取值范圍.11.設(shè)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在SKIPIF1<0處取得最大值,求a的取值范圍.12.已知函數(shù)SKIPIF1<0(SKIPIF1<0).(1)討論函數(shù)SKIPIF1<0的單調(diào)性;(2)若關(guān)于SKIPIF1<0的不等式SKIPIF1<0在SKIPIF1<0上恒成立,求實(shí)數(shù)SKIPIF1<0的取值范圍.13.已知函數(shù)SKIPIF1<0.(1)討論SKIPIF1<0的單調(diào)性;(2)當(dāng)SKIPIF1<0時(shí),函數(shù)SKIPIF1<0在其定義域內(nèi)有兩個(gè)不同的極值點(diǎn),記作SKIPIF1<0、SKIPIF1<0,且SKIPIF1<0,若SKIPIF1<0,證明:SKIPIF1<0.14.已知實(shí)數(shù)SKIPIF1<0,函數(shù)SKIPIF1<0,SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)性;(2)若SKIPIF1<0是函數(shù)SKIPIF1<0的極值點(diǎn),曲線SKIPIF1<0在點(diǎn)SKIPIF1<0?SKIPIF1<0(SKIPIF1<0)處的切線分別為SKIPIF1<0?SKIPIF1<0,且SKIPIF1<0?SKIPIF1<0在y軸上的截距分別為SKIPIF1<0?SKIPIF1<0.若SKIPIF1<0,求SKIPIF1<0的取值范圍.15.已知函數(shù)SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)性;(2)若SKIPIF1<0,函數(shù)SKIPIF1<0在SKIPIF1<0上恒成立,求證:SKIPIF1<0.16.設(shè)SKIPIF1<0,其中SKIPIF1<0是不等于零的常數(shù),(1)寫出SKIPIF1<0的定義域;(2)求SKIPIF1<0的單調(diào)遞增區(qū)間;17.已知SKIPIF1<0,函數(shù)SKIPIF1<0.(SKIPIF1<0為自然對(duì)數(shù)的底數(shù)).(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間;(2)求函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值.18.已知函數(shù)SKIPIF1<0.(1)若函數(shù)SKIPIF1<0在SKIPIF1<0處取得極值,求曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程;(2)討論函數(shù)SKIPIF1<0的單調(diào)性;(3)當(dāng)SKIPIF1<0時(shí),SKIPIF1<0,證明:函數(shù)SKIPIF1<0有且僅有兩個(gè)零點(diǎn),且兩個(gè)零點(diǎn)互為倒數(shù).19.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)若函數(shù)SKIPIF1<0有兩個(gè)極值點(diǎn)SKIPIF1<0,證明;SKIPIF1<020.(1)已知函數(shù)f(x)=2lnx+1.若f(x)≤2x+c,求c的取值范圍;(2)已知函數(shù)SKIPIF1<0.討論函數(shù)SKIPIF1<0的單調(diào)性.21.已知函數(shù)SKIPIF1<0(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間;(2)當(dāng)SKIPIF1<0時(shí),證明:對(duì)任意的SKIPIF1<0.22.設(shè)函數(shù)SKIPIF1<0,SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)性;(2)如果對(duì)于任意的SKIPIF1<0,都有SKIPIF1<0成立,試求SKIPIF1<0的取值范圍.23.已知函數(shù)SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)性;(2)若SKIPIF1<0存在兩個(gè)極值點(diǎn)SKIPIF1<0,SKIPIF1<0,求證SKIPIF1<0.24.已知函數(shù)SKIPIF1<0.(1)討論SKIPIF1<0的單調(diào)性;(2)當(dāng)SKIPIF1<0時(shí),SKIPIF1<0,求a的取值范圍.25.設(shè)函數(shù)SKIPIF1<0,SKIPIF1<0,SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)性;(2)若SKIPIF1<0,SKIPIF1<0,總有SKIPIF1<0成立,求實(shí)數(shù)t的取值范圍.26.已知函數(shù)SKIPIF1<0,其中e是自然對(duì)數(shù)的底數(shù),SKIPIF1<0.(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間;(2)當(dāng)SKIPIF1<0時(shí),求函數(shù)SKIPIF1<0的最小值.27.已知函數(shù)SKIPIF1<0,SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)性;(2)若當(dāng)SKIPIF1<0時(shí),方程SKIPIF1<0有實(shí)數(shù)解,求實(shí)數(shù)SKIPIF1<0的取值范圍.28.已知函數(shù)SKIPIF1<0,SKIPIF1<0.設(shè)SKIPIF1<0(1)試討論函數(shù)SKIPIF1<0的單調(diào)性.(2)若對(duì)任意兩個(gè)不等的正數(shù)SKIPIF1<0,都有SKIPIF1<0恒成立,求實(shí)數(shù)SKIPIF1<0的取值范圍;29.已知函數(shù)SKIPIF1<0.(1)討論SKIPIF1<0的單調(diào)性;(2)是否存在SKIPI
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