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1、2010年高考数学压轴题跟踪演练系列四Preparingforthe2010collegeentranceexaminationmathematics一一thefinaltitletrackingexercisesseriesfour(theonly1.outof14)Knownf(x)=(x,R)intheinterval[-1]isanincreasingfunction.(I)asetofvaluesoftherealnumbera;A;(II)setaboutXequationf(x)twononzerorealrootfo
2、rxl,x2.二ask:istherearealm,m2+tm+l二
3、xl-x2
4、makesinequalityforarbitraryaandAandT[1,1]permanentestablishment?Ifitexists,askfortherangeofM;ifnot,explainthereasonThistextmainlyexaminesthemonotonicityofthefunction,theapplicationofderivativeandinequalityandotherrelevantknowled
5、ge,examinethecombinationofnumberandshapeandclassificationdiscussionideaandflexibleuseofmathematicalknowledgetoanalyzeandsolveproblems・Thefullscoreis14.Solution:(I)f(x)==,DreamsofF(x)in[-1]isanincreasingfunction,*f'(x)=0forXand1][1,permanentestablishment,X2ax2islessthan
6、orequalto0ofX,[-1,1]permanentestablishment.Set(x)=x2ax2,Methodone:(1)=la2二0,1-1二a二1,(1)二l+a2二0.Forx二1[imprisonment,1],f(x)isacontinuousfunction,andonlywhena=l,f(-1)=0aswellasa=-1,f(1)=0LA={a
7、1=a=1}・methodtwo:Morethan0<0,Or(1)=l+a2二0(1)=la2=00=a=l=a=0orlForx二1[imprisonm
8、ent,1],f(x)isacontinuousfunction,andonlywhena=l,f(-1)=0,whena=-l,f(1)=01}.LA={a(II)toX2ax2二0by二，Delta二a2+8>0,dreamsLxl,axx2x2equation2=0twonon-zerorealroots,Xl+x2二a,Lto
9、xlx2
10、=.Xlx2=2,Dreams-1=a=1,
11、xl~x2
12、==3.*Tomakethem2+tm+lmorethan
13、xlx21inequalityforarbitrarya,AandTin
14、[1,1]permanentestablishment,Ifandonlyifm2+tm+l二3foranyt[1,1]permanentestablishment,Them2+tm2ismorethan0ofanyt[1,1]・ThepermanentestablishmentLetg(T)二m2+tm-2二mt+(M2-2)beestablished,Methodone:G(1)=m2m2二0,G(1)=m2+m2二0,M=2orM=2.So,therearerealm,m2+tm+l二xl-x2inequalityforarb
15、itrarya,AandTin[1,1]constantwasestablished,itsrangeis{m
16、m二2,orM二2}・Methodtwo:Whenin二0,itisclearlynotestablished;Whenm=0,M>0,m<0,OrG(1)=m2m2=0g(1)=m2+m2二0M=2orM=2.So,Therearerealm,m2+tm+l二
17、xl-x2
18、inequalityforarbitrarya,AandT,[-1,1]constantwasestablished,itsrangeis{m
19、m二2
20、,orM=2}.(theonly2.outof12)AsshowninfigureP,Q.isthepointontheparabolaC:y=x2,thelineLisoverP,andtheparabolaCisatanother
