高中数学高考总复习函数的单调性与最值习题及详解

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1、高考总复习高中数学高考总复习函数的单调性与最值习题及详解一、选择题1．已知f(x)＝－x－x3，x∈[a，b]，且f(a)·f(b)<0，则f(x)＝0在[a，b]内(　　)A．至少有一实数根B．至多有一实数根C．没有实数根D．有唯一实数根[答案]　D[解析]　∵函数f(x)在[a，b]上是单调减函数，又f(a)，f(b)异号．∴f(x)在[a，b]内有且仅有一个零点，故选D.2．(2010·北京文)给定函数①y＝x，②y＝log(x＋1)，③y＝

2、x－1

3、，④y＝2x＋1，其中在区间(0,1)上单调递减的函数的序号是(　　)A

4、．①②B．②③C．③④D．①④[答案]　B[解析]　易知y＝x在(0,1)递增，故排除A、D选项；又y＝log(x＋1)的图象是由y＝logx的图象向左平移一个单位得到的，其单调性与y＝logx相同为递减的，所以②符合题意，故选B.3．(2010·济南市模拟)设y1＝0.4，y2＝0.5，y3＝0.5，则(　　)A．y3

5、4．(2010·广州市)已知函数，若f(x)在(－∞，＋∞)上单调递增，则实数a的取值范围为(　　)A．(1,2)B．(2,3)integratedenergy,chemicalsandtextileYibincity,arethethreecorepillarsoftheindustry.In2014,thewuliangyebrandvalueto73.58billionyuan,thecity'sliquorindustrysliptostabilise.Promotingdeepdevelopmentofintegrat

6、edenergy,advancedequipmentmanufacturingindustry,changningdistrict,shalegasproductioncapacityreached277millioncubicmetres,builtthecountry'sfirstindependenthigh-yieldwellsandpipelinesinthefirstsection,theleadinfactoryproductionandsupplytothepopulation.2.1-3GDPgrowthfig

7、ure2.1-4Yibin,Yibincity,Yibincity,fiscalrevenuegrowth2.1.4topographyterrainoverallisSouthwest,North-EasternState.Lowmountainsandhillsinthecitylandscapeasthemainridge-and-Valley,pingbasmallfragmentednaturepicturefor"waterandthesecondlandofthesevenhills".236metersto200

8、0metersabovesealevelinthecity,lowmountain,46.6%hills45.3%,pingbaonly8.1%.2.1.5developmentofYibinlandscapesanddistinctivefeatureinthecenterofthecity,withlimitations,andspatialstructureoftypicalzonalgroup,2012-citiesinbuildingwithanareaofabout76.2km2.Fromcity-buildings

9、ituation,"oldtown-theSouthBank"Centerconstructionislaggingbehind,disintegrationoftheoldcityisslow,optimizationandupgrading,qualitypublicserviceresourcesarestillheavilyconcentratedintheoldtowntogether.SouthbankCentrehasnotbeenformed,functionsoftheserviceareaspaceismis

10、sing.Meanwhile,peripheralgroupcentresservicewasweakandinadequateaccountingforcitydevelopment,"suspicious"patterncouldnotbeformed.As