导数的应用二——恒成立问题的解题策略

ofvisionYibinformationintheCentersurroundedby,organicdispersionbandofbead-spacelayoutstructure,asleadingdevelopmentofthecitytotheEastalongtheYangtzeRiver.ShiGuarea,lingangnewvisiontoexpand,NaxidistricttotheNorth,theEastopenplacestoexpand,Jianganeastwardconnection,PingShan,radiationtotheWest;theSouthBankarea,theminjiangRiverarea,GoldenSandsareaonalong-termbasisinareasonablespacetodevelop,perfecturbandistrictalongtheYangtzeRiverinYibinRibbonmulti-centerstrategicvisionofspaceframe.YibinCenterCitydevelopmentconstructionsteeringextensiontypeextendedandconnotationtypeupgradesimultaneouslyofmode,inMetroconstructionofwhileiscommittedtooldcitytransformationandbuiltdistrictofperfect,throughliveandindustrywithtoofreasonablelayoutoptimizationcitystructure,improvecitytrafficoperationefficiency;vigorouslyimprovedcityenvironment,shapingcityfeatures,upgradecityquality,playcityofservicefunction,formedhasperfectmodernservicecapacityofbigcity.Constructionofurbangreenspacesystem,promotingtheconstructionofperipheralgreenspaceandprotectionofhistorical导数的应用二——恒成立问题的解题策略一．典例分析提炼方法例1．若不等式xax312，对任意的0x恒成立，求实数a的取值范围。变式训练1．若不等式013222aaxx对任意的]1,1[x恒成立，求实数a的取值范围。2．若不等式223221ccxxx对任意的]2,1[x恒成立，求实数c的取值范围。3．若不等式322231xbaxx对任意的),0[x恒成立，求实数b的取值范围以及a与b满足的关系式。二．考题训练形成能力1．设函数.0ln22aaxxxaxf，）（(I)求)(xf的单凋区间：(Ⅱ)求所有实数a，使e，2)(1exf对ex,1恒成立。注；e为自然对数的底数。2．设函数1ln1xxxf，若对所有的0.x都有axxf成立，求实数a的取值范围.ofvisionYibinformationintheCentersurroundedby,organicdispersionbandofbead-spacelayoutstructure,asleadingdevelopmentofthecitytotheEastalongtheYangtzeRiver.ShiGuarea,lingangnewvisiontoexpand,NaxidistricttotheNorth,theEastopenplacestoexpand,Jianganeastwardconnection,PingShan,radiationtotheWest;theSouthBankarea,theminjiangRiverarea,GoldenSandsareaonalong-termbasisinareasonablespacetodevelop,perfecturbandistrictalongtheYangtzeRiverinYibinRibbonmulti-centerstrategicvisionofspaceframe.YibinCenterCitydevelopmentconstructionsteeringextensiontypeextendedandconnotationtypeupgradesimultaneouslyofmode,inMetroconstructionofwhileiscommittedtooldcitytransformationandbuiltdistrictofperfect,throughliveandindustrywithtoofreasonablelayoutoptimizationcitystructure,improvecitytrafficoperationefficiency;vigorouslyimprovedcityenvironment,shapingcityfeatures,upgradecityquality,playcityofservicefunction,formedhasperfectmodernservicecapacityofbigcity.Constructionofurbangreenspacesystem,promotingtheconstructionofperipheralgreenspaceandprotectionofhistorical23．设函数1)(2xxf对任意),23[x，)(4)1()(4)(2mfxfxfmmxf恒成立，则实数m的取值范围是___________4.已知函数0,11)1(1)(xxxaxnxf其中0a(I)若xf在1x处取得极值，求a的值.（Ⅱ）求xf的单凋区间.（Ⅲ）若xf的最小值为1.求a的取值范围.三．反馈练习总结提升1.设)1(2xaxexfx,且曲线)(xfy在1x处的切线与x轴平行．(I)求a的值，并讨论)(xf的单调性：(II)证明：对]2,0[,不等式2|)(sin)(cos|ff恒成立。2．设函数1)1(233)(23xaxxaxf,其中a为实数．(I)已知函数)(xf,在1x处取得极值，求a的值：(Ⅱ)已知不等式1)(2axxxf对任意),0(a都成立，求实数x的取值范围．3．已知函数)(11ln)(Raxaaxxxf(I)当21a时，讨论)(xf的单调性(II)设42)(2bxxxg．当41a时，若对任意)2,0(1x,存在]2,1[2x,使)()(21xgxf,求实数b取值范围．ofvisionYibinformationintheCentersurroundedby,organicdispersionbandofbead-spacelayoutstructure,asleadingdevelopmentofthecitytotheEastalongtheYangtzeRiver.ShiGuarea,lingangnewvisiontoexpand,NaxidistricttotheNorth,theEastopenplacestoexpand,Jianganeastwardconnection,PingShan,radiationtotheWest;theSouthBankarea,theminjiangRiverarea,GoldenSandsareaonalong-termbasisinareasonablespacetodevelop,perfecturbandistrictalongtheYangtzeRiverinYibinRibbonmulti-centerstrategicvisionofspaceframe.YibinCenterCitydevelopmentconstructionsteeringextensiontypeextendedandconnotationtypeupgradesimultaneouslyofmode,inMetroconstructionofwhileiscommittedtooldcitytransformationandbuiltdistrictofperfect,throughliveandindustrywithtoofreasonablelayoutoptimizationcitystructure,improvecitytrafficoperationefficiency;vigorouslyimprovedcityenvironment,shapingcityfeatures,upgradecityquality,playcityofservicefunction,formedhasperfectmodernservicecapacityofbigcity.Constructionofurbangreenspacesystem,promotingtheconstructionofperipheralgreenspaceandprotectionofhistorical34．已知函数.1ln)1()(2axxaxf(I)讨论函数)(.xf的单调性：(II)设2a,证明：对任意,0,21xx,||4|)()(|2121xxxfxf5.设函数)10(ln1)(xxxxxf且(I)求函数)(xf的单调区间；(II)已知axx12,对任意)1,0(x成立，求实数a的取值范围。6.已知)(22)(2Rxxaxxf在区间[-1，1]上是增函数。(I)求实数a的值组成的集合A：(II)设关于x的方程,xxf1的两个非零实根为21,xx,试问：是否存在实数m。使得不等式||1212xxtmm对任意的Aa及]1,1[t恒成立?若存在，求m的取值范围；若不存在，请说明理由．ofvisionYibinformationintheCentersurroundedby,organicdispersionbandofbead-spacelayoutstructure,asleadingdevelopmentofthecitytotheEastalongtheYangtzeRiver.ShiGuarea,lingangnewvisiontoexpand,NaxidistricttotheNorth,theEastopenplacestoexpand,Jianganeastwardconnection,PingShan,radiationtotheWest;theSouthBankarea,theminjiangRiverarea,GoldenSandsareaonalong-termbasisinareasonablespacetodevelop,perfecturbandistrictalongtheYangtzeRiverinYibinRibbonmulti-centerstrategicvisionofspaceframe.YibinCenterCitydevelopmentconstructionsteeringextensiontypeextendedandconnotationtypeupgradesimultaneouslyofmode,inMetroconstructionofwhileiscommittedtoold