高考题汇编函数

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2010
ὃᦪ⚪ᑖᦪ(2010ᦻᦪ)17.ᜩlgx+x=2Ḅ"#ᑣ/&'()()(A)(0,1).(B)(1,1.25).(C)(1.25,1.75)(D)(1.75,2)"᪆•4᪀⌼ᦪ/'(x)=lgx+8-2,ᵫ/(L75)=/(()=1g/—;<0/(2)=?2>0AB&'()(1.75,2)(2010Cᓭᦻᦪ)8.ᦪy=ax?+bxJy=logL,x(ab#0,|a|#|b|)ᙠPQRᙶ᪗UVḄττaWXYZD(2010Cᓭᦻᦪ)3.[ᖪ]├_`y(a)J├_bcx(ᐗ/a)efᐵ#ᑣᐸijYZAAA.y=-10x+200B.y=10x4-200C.y=-10x-200D.y=10x-200

1(2010lmᳮᦪ)(10)oᦪḄpᔠP=,2r☢tḄpᔠQ=<(x,y)x=-L,0,g,l;y=-1,0,1),ᑣᙠPQRᙶ᪗UV#PVᦪ/*)ḄWvាxyz஺V|}tḄᦪḄ}ᦪ(A)4(B)6(C)8(D)10"᪆4a=0,b=0;a=0,b=l;a=L,b=0;a=L,b=l;a=l,b=-l;a=4l,b=4l⚪#ᦑᫀ⌱B,⚪:22⌕ὃᦪḄᭆஹஹஹWXᦪᦪḄfᐵAt#ᦪᨵ
⌕#ZḄὃ#&V᫏⚪1c_1ஹ(2010ᐰ£ᔁ2ᳮᦪ)(10)¥¦y=x2ᙠt஺2ᜐḄᑗ¦J|}ᙶ᪗©ᡂḄ«R¬Ḅ\7☢®¯18,ᑣ஺=(A)64(B)32(C)16(D)8ூᫀ௃Aூ³⚪W௃⚪⌕ὃ´µ¶ᑣஹµᦪḄ·¸ஹᑗ¦Ḅ¶«R¬Ḅ☢®¹#ὃ´ὃºḄ»¼Z..1_31_3_11_3ூ"᪆௃y=-±x2,./=2,ᑗ¦y-a2=a2(X_Q),ÀÁ=0#a2223Â1Q—y--a2,Ày=0,x=3a,L•«R¬Ḅ☢®s=—3a—a2=18,"Ã஺=64.ᦑ⌱A.222(2010ᐰ£ᔁ2ᳮᦪ)(2).ᦪy=«ÄÅD(x>l)ḄÆᦪ(A)>=e2-'+l-l(x>0)(B)>-=e2x+l+l(x>0)>(C)y=e2j+l-l(xeR)(D)y=e2x+'+l(xeR)

2ூᫀ௃Dூ³⚪W௃⚪⌕ὃÆᦪḄ¶ÊᢣᦪᦪJᦪᦪḄÌᓄ஺ூ"᪆]ᵫÏᦪ"Ãx=e"T+l,ᓽFT(X)="+1,ÔX>LL.X_1>0,LÅln(x-l)wR#ÅJEK,.•.ᙠÆᦪVxcK,ᦑ⌱D.(2010▷Üᦻᦪ)10.[᪥⌕Þߺà⊤ᜧã#äᔜæç10èé⌱êà⊤#ᔜæèᦪ◀ì10Ḅíᦪᜧî§ðñ⌱êà⊤.òó#ᔜæYé⌱à⊤èᦪyJôæèᦪxõ)ḄᦪᐵUᵨ÷᦮ᦪy=[x]([ᑗ⊤úûᜧ'xḄᨬᜧ᦮ᦪ)Yì⊤ú¯[B]#ýx..…ஹx+3,,ஹx+4,7x+5,rrrnr(A)y=[-](B)y=[-------](C)y=[--------](D)y=[-------]10101010᪆ᱯx=56,y=5,᣸◀CஹI),x=57,y=6,᣸◀A,ᡠ&⌱B)*x=10஻?+a(0WaW9),0Wa<61x++"=]=m=—,.ioJLioJLio.x+3a+3x260,y>0,Aᦪ/'(x)OPf(*+y)=f(x)F(y)”ḄT[C](A)VAᦪ(B)HᦪAᦪ(C)ᢣᦪAᦪ(D)XYAᦪ᪆Z⚪ὃ]☠Ḅ_`ឋFf(x)f(y)=axay=ax+y=f(x+y)4(2010abᦻᦪ)(12)cdePᙠhiy=-----jakhiᙠePᜐḄᑗiḄnopᑣe*+1aḄtTu[0,[)(B)[?,g)(C)(D)wಘ4422444I᪆⌱D.y'=———=--------->2,/.-1

3᪆⌱A.L+L=iogm2+log,“5=k)g,“10=2,..Hi2=10,•.>O,..”=V1Kab(2010abᦻᦪ)(4)cda>0,Aᦪ஻x)=ax2+bx+c,x0OPᐵxḄ2ax+b=0,ᑣ=ᑡ⌱⚗Ḅ⚪BkᎷ⚪ḄT(A)BXGR,f(x)/(X)00(C)VXG/?,/(X)/(x)00᪆⌱C.Aᦪ/(x)ḄᨬT"-2)=/(%)2aVxwR,/(x)2/(Xo),ᡠ&⚪C┯.4(2010abᳮᦪ)(1O)cdePᙠhiy=--------jakhiᙠePᜐḄᑗiḄnopᑣ஻/+1ḄtT7V7Cᐔஹ7t3ᐔஹ3ᐔr(A)[0,—)ᓃ,(ߟ,—](D)442244ூᫀ௃Dூ⚪J௃Z⚪ὃ]ᦪḄJ_`&pAᦪḄd¡஺ூ᪆௃£ky=-----------=--------------->-1,ᓽtana¥T,ᡠ&%(e+1)'e'+2+e4(2010ᐰ¨ᔁ2ᦻᦪ)(7)hi>=/+ª+/?ᙠe(0,6)ᜐḄᑗiTx—y+l=0,ᑣ(A)a-\,b=\(B)a=-\,b-1(C)a(D)ூ᪆௃AZ⚪ὃ]ᦪḄJ«ᓽhijeᜐḄᑗi...y=2x+a[r=o="...a-1(°/)ᙠᑗix-y+l=஺.b-1(2010ᐰ¨ᔁ2ᦻᦪ)(4)Aᦪy=l+ln(x-D(x>l)Ḅ®AᦪT(A)y=e'+l-l(x>0)(B)¯=°+l(x>0)(C)y=ex+l-l(x€R)(D)y=ex~l+l(xeR)ூ᪆௃DZ⚪ὃ]AᦪḄ®AᦪᢣᦪHᦪḄ±ᓄAᦪ¥=HIN(³4)01),)

4ln(x-1)=y-1,x-1=,y=ex-'+1(2010´9ᳮᦪ)12.᝞¶C·¸p¹ↈᱏ(ᐸH½¾¿À☢ᚖÃ)ᒴÅᙢᓣÈÀ☢Ét1ʸp¹☄ÈÀ☢ÌᑖḄ¶Î☢ÏkS”)(S(0)=0),ᑣAᦪy=S'(f)Ḅ¶ÐᜧÒkBூÓᫀ௃Aூ᪆௃Z⚪ὃ]Aᦪ¶Ðஹᦪ¶ஹᦪḄÕ▭Jd¡×eὃ]ḄTHᦪØḄÙÚÛÜÝÞᵨÛÜ஺ᨬàá1ÊÝᨬâãe1Êäᨵåᓄᦪá᣸◀Cæ☢ÏÃçᢝéêäᨵëḄᦋåí᣸◀BὃîAஹDḄïðᙠñòóôḄᦋåTᔲö÷ὃ⇋ᑮᦪḄJ,ᑨûü1☢Ïᦋåkýå°þBû⌱ÿA஺(2010
ᳮᦪ)9.ᑡ⚪জᦪy=—In-~y_jtanᦪn21+cosx2ঝᦪy=/(x)y=g(x)Ḅᐵy=x!ᑣᦪy=f(2x)y=g(x)Ḅ#ᐵy=x$ঞ᜻ᦪ/(x))*+ᑁ-.x/ᨵ/(x)=/(2-x),ᑣ/(x)1ᕜ3ᦪ஺ᐸ56⚪A.জ@B.জঞC.ঝঞD.ঝூ8ᫀ௃Cூ;᪆௃ὃ>?ᦪஹᦪឋḄᑨCஹᕜ3ឋDE஺ὃ⇋)*+G!জ┯I$᣸◀AஹB,LMঞ!/(X)=/[2-(O)]=/(2+O),TUV᜻ᦪW஻X)=//),ᡠZf(x)ᕜ312Ḅᕜ3ᦪ!⌱\C஺(2010]^ᦻᦪ)(7)`a=(1)5,b=(*)5,c=(*)5,ᑣa,b,cḄᜧbᐵc555(A)a>c>b(B)a>b>c(C)c>a>b(D)b>c>a7.A

5*2ூ;᪆௃^=᮱ᙠg>0jkᦪ!ᡠZ஺>஺!l=m1o,ᙠg>0jpᦪ!ᡠc>b஺ூqrst௃᪷vwᦪᢣᦪᦪḄᓫzឋ{|ZᑨCᩭ.2010]^ᦻᦪom6o`abc>0,ᦪ/mgo=Z2+r+஺Ḅ|6.Dbூ;᪆௃஺>0j;bஹc!mComDo5c<0,ᦑ஺<0,——>0,⌱⚗mDoᔠ2aூqrᢈ௃᪷vᦪᔣᡈᔣ!ᑖ4>0ᡈ4<0ᑖὃ⇋.᜜¡⌕£.c¤¥ᱥy¨©ªḄ«ᙶ᪗!¡⌕£.¨Ḅ®¯ᡈ)ªᙶ᪗Ḅ®¯°.m2010±²ᦻᦪom4oᦪy=J16-4'Ḅ¤+(A)[0,+oo)(B)[0,4](C)[0,4)(D)(0,4);᪆º/4'>0,/.0<16-4'<16/.V16-4ve[0,4)(2010¾
ᦻᦪ)(9)ÀDxᦪf(x)=2'+ÃḄĪ.X|G(1,x),01-xxe(x,+8),ᑣ2o(A)f(x)<0,f(x)<0(B)f(xJ<0,f(x)>0(22(C)f(x)>0,f(x)<0(D)f(x,)>0,f(x)>0122;᪆⌱B,ὃÉÊᦪËtᔠḄÌÍ!ZÎᦪĪḄᭆÐÑĪḄᑨC!Ò5᫏⚪

6(2010¾
ᦻᦪ)2.ÀDᦪ/஺)=1(^(g+1),/஺)=1,a=(A)o(8)1(C)2(D)3;᪆a+1=2,ᦑa=i,⌱B,Ô⚪Õ⌕ὃÉÊᦪᦪᭆÐÎᐸÖ×ឋØ!ÒÙ᧕⚪(2010±²ᳮᦪ)মᦪ஻X)=—ᔆḄÝA.ᐵÞªB.ᐵy=xC.ᐵx¨D.ᐵy¨4~x+11+4,;᪆/(-x)=—ᔆ=—ß=/(x).•./(X)Ꮤᦪ!ᐵy¨(2010áâᦻᦪ)(11)ᦪy=2-/Ḅᜧã8ᫀA(2010áâᦻᦪ)(8)ÀDwäåᔆæḄçᑭéy(ᓫ®êᐗ)çåìí(ᓫ®êî)Ḅᦪᐵcï1^=-^/+85234,ᑣðñäåᔆæòWᨬᜧçᑭéḄçåì1(A)13êî(B)llêî(C)9êî(D)7êî8ᫀC(2010áâᦻᦪ)(5)`/(x)1)*ᙠRḄ᜻ᦪ!xNOBô!f(x)=2x+2x+b(bõᦪ)!ᑣ/(1)=(A)-3(B)-1(C)1(D)38ᫀA(2010áâᦻᦪ)(3)ᦪ஻X)=10g2(3'+l)Ḅ¤+1A.(0,+°°)B.[஺,+8)C.(1,4-0°)D.[1,+8)8ᫀA

7(2010ᓅ÷ᦻᦪ)(6))ᦪজ>=#!ঝy=log1(x+l),@y^x-U,টy=2"L35ᙠúû(0,1)ᓫz⌴pḄᦪý(A)জঝ(B)ঝঞ(C)ঞট(D)জট8ᫀB(2010ᓅ÷ᦻᦪ)ভa,bÿᔣ/ᑣᦪ/(x)=(xa+b>(xb-a)(A)ᦪ᜻ᦪ(B)ᦪ᜻ᦪ(C)ᦪᏔᦪ(D)ᦪᏔᦪᫀA(2010ᳮᦪ)(4)ᦪ/(x)=x2+mx+lḄᐵ!"x=l#$Ḅᐙ⌕ᩩ((A)in=—2(B)m=2(C)m=—1(D)in=1)᪆ᦪ/(x)=+-x+1Ḅ#$./X=-5,0=1=>m=-2ᫀA(2010ᳮᦪ)(3)2log10+log0.25=55(A)0(B)1(C)2(஺)4)᪆2/2510+/஺30.25=log\00+log0.2555=log255=2ᫀC(2010ᳮᦪ)(2)4ᑡ6ᡠ⊤9Ḅᦪᙠ;x=0ᜐ=>Ḅ(A)(D))᪆ᵫ@Aᦪ=>ḄឋCD஺EF.ᫀ஺(2010ᜩIᦻᦪ)(10)Kᦪg(x)=x2-2(xeR)_/g(x)+x+4,x

8999(A)--,0(1,+°°)(B)[0,+°°)(C)[—,+°°)(D)---,0kJ(2,+°°)444ூᫀ௃Dூ)᪆௃`⚪b⌕ὃdᦪᑖfᦪLMḄg`hijk⚪஺x'—2+(x+4),x2s⚪tD/(x)x?2x?—2—x,-1WXW2(2010ᜩIᦻᦪ)(6)Ka=1(^4,b=(log3)2,c=log/,ij5(A)a0,ᡠ;ᙠ³´(0,1)·⌱Cூ9௃ᦪ;▬¹ᦪLḄº»¼½¾f⌱¿⚪ÀᵨÁᐭ᣸◀Ḅih)஺

9logx,x>0,2(2010ᜩIᳮᦪ)(8)Æᦪf(x)=L'(_x),x<0Æf(a)>f(-a),ᑣÉᦪaḄÊLÌ(A)og.2(-1,0)U(0,1)(B)(-8,-1)U(l,+oo)(C)(-1,0)U(l,+8)(D)(-8,-1)u(0,1)ூᫀ௃Cூ)᪆௃`⚪b⌕ὃdᦪḄ#ᦪḄᓫឋஹ#ᦪḄg`ÏÐAᑖfÑÒÓÔjÕ⚪஺ᵫᑖÖᦪḄ⊤×ØD◤⌕#aḄEÚᑖfÑÒ஺a>0fa<0fভ>f(~a)='loga>log,aᡈ'logே(-a)>log(-a)22ஹ22a>0a<0=>\1ᡈ<1=>a>l^t-1——

10ூ)᪆௃`⚪b⌕ὃdᦪ;Ḅᭆ¨©;²ᳮḄ¶ᵨj᧕⚪஺ᵫ/(1)=í3<0,/(0)=1>0A;²ᳮDf(x)Ḅ;ᙠ³´(-1,0)·஺ூ9௃ᦪ;▬¹ᦪLḄº»¼½¾f⌱¿⚪ÀᵨÁᐭ᣸◀Ḅih)஺(2010îïᳮᦪ)3.Æᦪ/(x)=3ஹ+3"©g(x)=3*-3*Ḅ²¯Mᙳ/R,ᑣA./(x)©g(x)ᙳ/ᏔᦪB./(x)/Ꮤᦪg(x)/᜻ᦪC./(x)©g(x)ᙳ/᜻ᦪDJ(x)/᜻ᦪg(x)/Ꮤᦪ3.D./(-x)=3r+3'=/(x),g(-x)=3r-3'=-g(x).(2010îïᦻᦪ)3.Æᦪ/(x)=3'+3r©g(x)=3"-3TḄ²¯Mᙳ/RᑣA/(x)©g(x)©ᙳ/ᏔᦪB/(x)/᜻ᦪg(x)/ᏔᦪC/(x)©g(x)©ᙳ/᜻ᦪD/(x)/Ꮤᦪg(x)/᜻ᦪ):ᵫf(-x)=3-*+3-J)=f(x),ᦑf(x)Ꮤᦪ᣸◀BஹCᵫ⚪tDᙊöᙠy.øù᣸◀AஹCᙠRfAOA஺û=á=1,ᦑ"=@=3=00=5,⌱D0A1120஺00ý(2010îïᦻᦪ)2ᦪ/(x)=lg(x-l)Ḅ²¯MA(2,+8)B(l,4-oo)C[l,4-oo)D[2,-H>o))X-1>0,ÿ>1,⌱B.x~+2x3x<0(2010ᦻᦪ)7.ᦪ/(x*Ḅᦪ()-2+Inx,x>0A.3B.2C.1D.0ூ&ᫀ௃Bூ)᪆௃+xWO./01+2%3=0)4x=-35

11+x>0./0-2+lnx=0)4x=100,ᡠ89:ᦪᨵ</⌱C஺ூ>⚪@A௃B⚪ὃDᑖFᦪḄGH/ὃDIᑖJKLḄᦪMNO஺(2010ᐰQᔁ1ᦻᦪ)S9:ᦪ/(x)=llgxl.UaHbY/f(a)=/@),\]+)Ḅ^_ab(A)(l,+oo)(B)[l,+o«)(C)(2,+oo)(D)[2,+8)7.Cூ>⚪@A௃Bg⚪h⌕ὃDjᦪᦪḄឋlஹᦪḄᓫoឋஹᦪḄ_p/ὃqᙠsBg⚪.᩽᧕vwaḄ^_a/xᑭᵨᙳ_|}~G4a+b=a+,22,x┯⌱D,b>⚪ὅḄaᵨᜐ.ூ)᪆1௃f(a)=f(b),ᡠ8|lga|=|lgb|,ᡠ8a=b()/ᡈ/?=,/ᡠ8a+b=a+1aa0fপ=1+1=2,ᓽa+bḄ^_ab(2,+8).0y---?¤(1,1).zᨬgxx2,¦(C)(2,+8)(2010ᐰQᔁ1ᳮᦪ)(10)9:ᦪ/U)=|lgx|.U0ᦪḄᓫAឋCDE.F56⚪G᧕IJaḄKDMNOPᑭᵨᙳDTUVWX4a+2b=a+->2>/2,YZ┯⌱]N^_`⚪ὅ᢬Ḅ◍▟.a2X4ef>ᦪF(x)=|lgx|ḄghNᵫf(a)=f(b),஺ீlbm0<4<1<ᓃN-lga=lg/?,.\ab=l,.a^2b=a+—,ὃoa22>ᦪy=x+—ḄᓫAឋpmNq0ᦪᓫA⌴tN.•.஺+2b=஺+—>3.ᦑ⌱C.xa(2010«¬ᦻᦪ)(2)ᦪ)/=/஺&IḄA®ᜧ°b

12&ᫀC(2010±ᓅᦻᦪ)5.ᦪy=/1Ḅ³´p71og(4x-3)05333A.(-,1)C(1,+8)D.(-,1)U(1,+8)44___4_ூ௃Aூ᪆௃ᵫlo4x-3)>04x-3>0ᦑA4log,x,x>0i(2010±ᓅᦻᦪ)3.9:ᦪ=ீ0ᑣ/(/(§))=11A.4B.C.-4D—44ூ&ᫀ௃Bூ)᪆௃᪷·ᑖFᦪ¸4ᔩº=ᑣ஻¾—y,ᡠ8B»¼.2010ÀÁᳮᦪ!11
ᦪᱏ2*-/ḄAÃᜧ°bூ&ᫀ௃A

13,,1ூ)᪆௃+x=2ᡈ4./2X-X=0,ᡠ8᣸◀BஹC5+x=-2./2X-X'=4<0,ᦑ᣸◀D,4ᡠ8⌱A஺ூ>⚪@A௃B⚪ὃDᦪḄA®/ὃDÊMËjᦪÌẠ:ÎḄÏÐÑÒ8ÓᦪÔÕᔠḄN×ØÙ஺(2010ÀÁᳮᦪ)(4)Úf(x)³´ᙠRḄ᜻ᦪ,+x20./f(x)=2*+2x+b(bÝᦪ),viJf(T)=(A)3(B)1(0-1(D)-3ூ&ᫀ௃Dூ)᪆௃f(x)³´ᙠRḄ᜻ᦪᡠ8ᨵf(0)=2°+2x0+b=0,)4b=-lᡠ8+x0.^)=2"+2x-lf(-l)=-f(l)=-(21+2w1-1)=-3ᦑ⌱ä.5:ூ>⚪@A௃B⚪ὃDᦪḄÌBឋl/åæᦪḄÌẠ:Îb)&çB⚪Ḅᐵé.(2010±ᓭᳮᦪ)8.ᵨë"{0/"⊤îa,b<ᦪïḄᨬg_஺Uᦪ=ḄAÃᐵðñx=-1jò/\UtḄ_2A.-2B.2C.-1D.1

14ூyᫀ௃b[ூX᪆௃ᵫ|gp}~fᐰ/(=0^.|w+N|ḄghᐵOᡃw=-1ᦪḄghNὃoὃᦪᔠḄ]N᫏⚪.2(2010ᳮᦪ)4ஹ஻]_RJLᕜ¡¢5Ḅ᜻>¤N¥⏀§"1)=1J«)=2,5M/(3)-/(4)=Aஹ¨1Bஹ1C\—2Dஹ2JLAூX᪆௃/(3)-/(4)=/(-2)-/(-I)=-/(2)+/(D=-2+1=-1.mSAூ©ªᢈ¬௃᪷®/(3)./(4)ᑖ¯°/(2)JপᨵᐵNᑭᵨ/(x)_RJtᕜ¡¢5Ḅ᜻>ᦪḄᕜ¡ឋ²(2010ᳮᦪ)6ஹ³஺´µ0,¶·>ᦪ஻¸=ᦪ2+¹+஺Ḅghp_

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16K᪆ὃa3ᦪᐵᭆஹឋ¡d-3ᦪ/(x)=log3(x+3)Ḅ3ᦪ?y=3*-3,x=0,ᨵy=-2d3ᦪ/(x)=log3(x+3)_x?(-2,0),ᑭᵨ$%ឋ¥Z3ᦪ/(x)=log3(x+3)Ḅ3ᦪḄ_yḄ?(0,-2)(2010¦ᓭᦻᦪ)10.YZSᩞᧇḄᨬ¬ᐭ¯ᙠ100gᑮ200g²³´ᵨ0.618dµ᣸m·,ᑣ¸S¹mḄᐭ¯¥XgூHᫀ௃171.8ᡈ148.2ூK᪆௃᪷»0.618d¸S¹mᐭ¯?110+(210-110)X0.618=171.8ᡈ210—(210-110)X0.618=148.2ூ]⚪_௃`⚪ὃ¼½⌱dḄ0.618d¾¿᧕⚪஺f3x+2,x1,K᪆/(0)=2,f(É(0))=f(2)=4+2a=4a,ᡠXa=2t2—4f+1(2010ÊËᦻᦪ)(12)YZf>0,ᑣ3ᦪÌ=•------------■ḄᨬÍ?.t/2—4/+11K᪆=-_2L_L=A_4>-2(V/>0),MÎÏMf=lPy=-2YZ+min(2010ÐÑᦻᦪ)(16)ÒᖪÔSᨴÖ×ØᨴÖÙÚ├ÜÝÞ3860ßᐗ⚜âãᨴÖ├ÜÝ?500ßᐗäᨴÖ├ÜÝåãᨴÖ⌴çX%,èᨴÖéÜÝåäᨴÖ⌴çX%,êஹᓝᨴÖ├ÜìÝäஹèᨴÖ├ÜìÝ)´Sᨴ×ᓝᨴÖ├ÜìÝ×í×íÞ7000ßᐗîïxḄᨬÍOHᫀ20(2010ÊËᳮᦪ)(15)YZ3ᦪf(x)ðñ/(1)=U4/(x)/(y)"(x+y)+/(x-y)(x,yeR),ᑣ“201஺)=.K᪆òx=ly=0T/(0)=gd—óôÚõ/(2),/(3),/(4)..........öTᕜø?6d:òx=ny=l,ᨵf(n)=f(n+l)+f(nl),ùᳮf(n+l)=f(n+2)+f(n)

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19ூ(ᫀ௃2஺Iூ,᪆௃ÜᱥËḄᯖØᙶ᪗EF(0,9)ᑣÛᯖØá᳛E1ḄÒËöET=x+f,஺22ø(ù¹ú)8(û¹/)(ᔛýù)ᵫ⚪RDÿ00஺_pᵫ"2y/-2Px-2P?=0-./=2ᑐ.ᵫᳮx+x,=2p,xx=-p2^tl2ᡠABCDḄ☢'(τS=1Gi+H)(஽-Ñ)=Ò(*Ó+¬+Ô)(ᔛ¨Ö)=)*ᔣ+,7.=:3*14P?+40eXX=342p25130P2=720,890,ᡠ᝞=2~1ூ=⚪?@௃B⚪ὃDEFḄᯖHᙶ᪗KFḄLMKFNOᱥFḄQRᐵTὃUὃVḄWXYZ[\᫏⚪-^ὃ_`abc(2010efᳮᦪ)15.jklm((0,+8)Ḅoᦪf(x)qrজtu?xe(0,+8),ឤᨵf(2x)=2f(x)ᡂy;{X஺஺,27|,f(x)=2-x«~᝞:জtu?meZ,ᨵf(2m)=0ঝoᦪf(x)Ḅm(0,+8)ঞᙠneZ,f(2-+l)=9ট“oᦪf(x)ᙠ(a,b)ᓫ⌴”Ḅᐙ⌕ᩩ“1ᙠkeZ,(a,b)G(2«,2*”஺ᐸ\ᡠᨵ¤¥Ḅ¦§஺ூ¨ᫀ௃জঝটூª᪆௃tজ¬(2m0,ᡠf(2m)=0,ᦑজ¤¥®ᑖ᪆°᧕ঝট²¤¥஺ூ=⚪?@௃B⚪ὃDoᦪḄឋ´Nᐙ⌕ᩩµ¶·Ạk¹ª¨ºB⚪Ḅᐵ»஺(2010¼½ᔁ)5ஹÀoᦪf(x)=x(e'+ae*)(xeR)ᏔoᦪᑣÅᦪ஺=ª᪆7ὃDoᦪḄ᜻ᏔឋḄk¹஺g(x)=e'+ae”(᜻oᦪÈg(0)=0,஺=É1஺

20x2+1"2°,5.(2010¼½ᔁ)11ஹjkoᦪ/“)=ᑣqrËÌÍ/(1É/)>/(2x)ḄxḄ1,x<0Ñ.2>2xª᪆7ὃDᑖÒoᦪḄᓫឋ஺\-x=>xe(-I,V2-1)\-x2>0(2010¼½ᔁ)14ஹÓÔÕ(1m¤Ö×ↈᱏÚᩩÛÜÝÞÔḄKFßᡂàᙽᐸ\-(ḄᕜÕ¥ᙽ,äS=ᑣsḄᨬè.Ḅ☢'ª᪆7ὃDoᦪ\ḄféêᵨÌìíᓄïð஺É⚪ñª஺ÀßᡂḄè¤Ö×ḄÔÕ(X,ᑣs=_____⁐ôõ______4(3-x)2=<1…÷”ஹ7T--(x+l)--y(1-X)(LøÉ)ᑭᵨúᦪûoᦪᨬè஺&(ஹ4(37)24(2X-6).(1-X2)-(3-X)2.(-2X)3(x)=—j=------ü3(1)=—j=---------------------------V31-X26(1")2=(2x-6)(l-x2)_(3-x)2.(-2x)=4-2(3x-l)(x-3)Éὡ(1f)2—ὡ(12)2S,x)=0,00,⌴;ᦑx=LSḄᨬ!"#$஺33('())ᑭᵨ,ᦪḄ'(.ᨬ!஺$J/91/3—x=fje(2,3),-e(3))ᑣ:t32G-r+6t-SG86--2---1ᦑ==3,x=sḄᨬ!"?@஺t833

212010ABὃᦪDE⚪ᑖHIJ,ᦪ(2010KLᦻᦪ)22.(O⚪Pᑖ16ᑖ)O⚪ᐳᨵ3S⚪T1⚪Pᑖ3ᑖT2⚪Pᑖ5ᑖT3⚪Pᑖ8ᑖ஺VWᦪxஹyஹ஻P[ᑣ\x]y^_`.(1)V/-I]3^_0,.xḄb!d(2)efghS3ijḄkᦪ஻ஹᓃmno஺2ᓃ+4/]/+63^_2rs(3)tu,ᦪ/(x)Ḅvwx஺y,஺᝕3{€2,}€/?}.fb}€஺/3)j1+sinxl-sinx^_0ḄS!.ᑏ,ᦪ/(x)Ḅ᪆ᢣḄ᜻Ꮤឋஹᨬkᕜஹᨬ!ᓫឋ(3⌕.mn).᪆oপxe(-2,2)ফefghS3ijḄkᦪaஹb,a2b+ab2>2ab\[ah,a+h3>2ab\[ab,Ia%+a/-2ab4abl-la3+/?3-2aby[abᓃ-(a+b){a-b)2<0,ᡠIa%+ab2-2abᲦl

22X(I)/(x)ḄE¢(0,+8).1y(x)¨×•+i+dl=l£±ᔩ±11.4JTXX(1)-௃0#q-avx1GN(x)>0.ᦑ/(X)ᑖ¯ᙠ(0,-a).(I.+8)ÚᓫA⌴ÛNᙠ(-0.1)ÚᓫA⌴t.(2)aᦪ.ÞßÚNS/i(x)-(-2x,+3ax2+6ar-4aJ-6a)e*(reR),ᑣ/»'(x)=(-2x,+3(fl-2)*l+12ar-4a2e,.ѳm(x)=-2x'+3(a-2)f+12ac-à(XGR),ᑣq8(m)ᙠá஺N-஺ÓÚᓫA⌴tGNA(x)âᙠá஺,0ÚᓫA⌴tNᡠ}"(a)wO.ᵫe'>0,äåm(a)W0.Zæ(a)=a'(a+2),ᡠ}aw-2.åGNçᯠᨵg(x)ᙠa,-aÚ¢t>ᦪNq¥éqf(x)ᙠÚ¢t>ᦪNFr)ᙠá%ÓÓÚ¢t>ᦪN¥Ml)Úeᵫ(I)mNqaW-2GN/(x)ᙠ1,-஺ÓÚ¢t>ᦪ.জëᐭপপ="+13a+3wO=-3WOW-ᓝ.ঝTïm⍝NVxea,,Af(i)^0<=>Vxefa.l,m(x)w0.Hff»,(r)=-6x2+6(a-2Jx+12a=-6(x+2)(x-a),ñò'(x>=0,ᑣx=a,ᡈx=-2.Za4-2,_(1)qav-2GNa0$¨2vxv1,ᑣm'(x)<0.äZm(x)ᙠ(a.-2)ÚᓫA⌴Û.ᙠ(-2,1)ÚᓫA⌴t.(2)q஺=-2GNm(x)W஺Nm(x)ᙠ(-2.1)ÚᓫA⌴t.

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MO)=O.ᓽª᜜°_—.aax+lnoaḄ;!²□³E.2ூ"´௃ᦪµ¶I·ὃḄ¸¹⚪ºὃḄN⌕»µ·¼⌕ὃᱞ¾¿ÀÁẠஹÁxᢈÄ⌕ὃᐹᨵÇÈḄᑖ᪆NN.É9ʺᦪḄὃNËÌ®Í஺¶I¸¹⚪⌕ÎDᑭᵨᦪᨬ!ឤᡂ¨⚪ᑭᵨᦪ|}µÑÒºᦪḄ¬ÓÔ"Õᡠᙠ.(2010▷×ᦻᦪ)21ஹ(xy⚪Fᑖ14ᑖ)Ù{ᦪf(x)=y[x,g(x)=alnx,aSR«(1)¢ßày=f(x)âßày=g(x)ãäᙠä"ᜐᨵãæḄᑗàaḄ!DèᑗàḄdé;

27(2){ᦪh(x)=f(x)-g(x),h(x)qᙠᨬyÕᐸᨬy!í(a)Ḅ᪆;(3)º(2)îḄ9(a),|}gae(0,+oo)0),2yJxxᵫÙòrVx=alnx,L_L-£öa=—,x=ee2yJxx21:ᩩßàä"Ḅᙶ᪗I(eee)ᑗàḄû᳛Ik=f'(e’⚗1gᑗàḄdéIy-e=27(x-e).2=Vx—fllnx(x>°),ফᵫᩩஹ',,ஹ1a_2a:•2=QR='Ia.>0A'ᑗ=0,X=4Q2,ᡠ041()ಘᙠ(0,+8)Ḅ/0᩽234(᩽563789(:তḄᨬ563஺ᡠজ(a)=h(4«2)=2a-aln4a2=2HaW஺/i(x)=(l/2-2a)/2x>0,h(x)ᙠ(0,+°°)⌴%,Fᨬ56஺ᦑh(x)Ḅᨬ56জ(a)Ḅ᪆IJ2a(lTn2a)(a>o)(3)ᵫ(2)জ(a)=2a(l-ln2a)ᑣজ'(a)=-21n2a,জ'(a)=0a=1/20ீa0,ᡠP(a)ᙠ(0,1/2)⌴%a>l/2জ'Q)<0,ᡠজঝ)ᙠ(1/2,+8)⌴!஺ᡠজQ)ᙠ(0,+8)ᜐU᩽ᜧ6জH/2)=1WJজQ)ᙠ(0,+8)ᨵ4Yᨵ0Z᩽23ᡠজ<1/2)=19(জ(a)Ḅᨬᜧ6

28ᡠa[\(0,+8)]ᨵP()W1a(2010^_ᦻᦪ)(21)(b5⚪dᑖ12ᑖ)fgᦪ/(X)=(a+Dlnx+ax+1.(I)jkgᦪ/(x)Ḅᓫmឋ;(II)paW-2,qrstuvwx2e(0,+8),I/(%1)-/(x)1>41-x1.22s(I)/(x)Ḅ{|}J஺+8),/0)="1+2=+"+1.XX,f\x)>0,ᦑ/(x)ᙠ(0,+8)ᓫm%;aW-lf\x)<0,ᦑ/(x)ᙠ(0,+8)ᓫm!;0lVaVO/'(x)=0,x=J-"LxG(O,/-^)f\x)>0"V2av2aXG(J—"1,+8)")<0,ᦑ/(x)ᙠ(0,J0⁐f)ᓫm%ᙠ(/0⁐+8)V2aV2aV2aᓫm!.(11)Ꮇp*12.ᵫ\02,ᦑᙠ(0,+8)ᓫm!.ᡠ|/(3)_/(%)|240/|\f(x)-f(x)24XI-4X2,t2ᓽ2)+4X22/(X1)+4*1.g(x)=/(x)+4x,ᑣ,஺+1g(x)=----F2ax+4x_lax1+4x+a+1x/ஹ—4+4x—1—(2x—1)~\(g(x)W-------------=--------WO.XX78g(8ᙠ(0,+8)ᓫm!,ᦑg(xWgd),ᓽ/(X1)+4X1W/(X2)+4X2ᦑtuvஹ1,X2£஺+8),|/(^1)-/(^)|>4|x,-X\.22

29
2010^_ᳮᦪ¤
21¥b5⚪dᑖ12ᑖ¤fgᦪ/
x=++ax2+1
Ijkgᦪ/
xḄᓫmឋ"¥II¤pQ<-1.᝞§tuv¨G
0,+°°Tτ/
^1¤-/
%¤241X]τ©஺ḄU6«஺2s¥I/*Ḅ{|}J¥0,+8¤.f'x
=-+2ax=2ax'+-^+].XX஺20fXx
>0,ᦑ/¥¬¤ᙠ¥0,+8¤ᓫm%"஺<01f\x
<0,ᦑ/¥X¤ᙠ
0,+8¤ᓫm!"1VQV0/'(x)=0,x=J-------V2aᑣ-0,5¤MK>஺…q-V,+8KWTXK<஺.ᦑ/¥X¤ᙠ
0,ஹ-Q■ᓫm%ᙠ
J—L+8¤ᓫm!.V2aV2a¥II¤Ꮇpᓰ2%8஻ீ-Iᵫ¥I¤ᙠ¥஺+°°¤ᓫm!78VXpXjG(0,+oo),|/(x)-y(x)|>4|x-x\1212\V%1,xG(0,4-oo),/(x)+4X>/(%1)+4x,জ222g(x)=f(x)+4xᑣg'(x)=^~^+2ax+4xজ\g(x)ᙠ(0,+°°)ᓫm!ᓽ1+2ax+4<0.xu8஻ீߟ©ߟ1(2x-l)2-4x2-2(2x-l)22/+12/+12X2+1ᦑaḄU6«J(-8,-2].……12ᑖ

30(2010ᐰ³ᔁ2ᦻᦪ)(21)(b5⚪dᑖ12ᑖ)fgᦪf(x)=x3-3ax2+3x+U(I)pa=2,©f(x)Ḅᓫm·¸"(II)pf(x)ᙠ¹¸(2,3)Pºᨵ0Z᩽63©aḄU6«஺ூ᪆௃b⚪ὃ¾rÀᦪᙠgᦪឋÁPḄÂᵨÄ⌕ὃ¾ÆᵨÀᦪẆÈgᦪḄᓫm¹¸ஹ᩽6ÉgᦪÊ)ËḄÌ஺(1)©QgᦪḄÀᦪᵫÀᦪᜧ\0,Í©%¹¸ᵫÀᦪ5\0,Í©!¹¸஺(2)©QgᦪḄÀᦪ/'(X),ᙠ(2,5ᑁᨵ᩽6ᓽJÆ‘(X)ᙠ(2,3)ᑁᨵ0ZÑ3ᓽÍ᪷Ó(2)-(3)<°,ᓽÍ©QÔÕU6«஺(2010Ö×ᳮᦪ)19.(b5⚪dᑖ12ᑖ)pgᦪ/(x)=lnx+ln(2-x)+ax(a>0)o(1)a=L©/(x)Ḅᓫm¹¸஺(2)Ù“X)ᙠ(0,1Ḅᨬᜧ6J:©aḄ6஺ூ᪆௃ὃ¾gᦪÀᦪÜÝஹᑭᵨÀᦪᜐᳮgᦪᨬ6Ì஺stgᦪ©Às/z(x)=-———+a,{|}J(0,2)x2-x(1)ᓫmឋḄᜐᳮàáÀᦪḄÑ3âãäᑨæçèéᡂ஺a=l/'(x)=oL001—+=0nT+2=0x2-xx(2-x)Xe(0,&),y'(x)>0,J%¹¸;Xe("2),í<0,J!gᦪ஺(2)¹¸(0,1Ḅᨬ6î⚪àáÀᦪᑮᓫmឋðᔠ᩽63wò3Ḅóôᑮõ{ö{÷aḄ6஺xe(0,1ᨵᨬᜧ6ᑣøJ!gᦪ4/'(x)=-——+a>0,Jᓫm⌴%¹¸஺x2—xᨬᜧ6ᙠùò3Uᑮ஺/ú=f(^)=a=~°(2010ûüᦻᦪ)20.(b5⚪dᑖ12ᑖ)pgᦪ/(X)=sinx-cosx+x+l,0

31ூ⚪௃⚪ὃᦪḄ!"ᑭᵨᦪẆ&ᦪḄᓫឋ᩽Ḅ()"ὃ*ᔠ,ᵨᦪ-./012⚪Ḅ34.ூ0⚪ᢣ௃(1)8ᦪ/(x)=sinx-cosx+x+l"8ᦪᵨ>?@ABCD"ᑭᵨᦪEF஺G᩽H"IJᑡ⊤Ḅ()ὃ᩽HḄMNᦪḄOP"ᑨRḄᓫឋ"᩽.0:ᵫf(x)=sinx-cosx+x+l,0

32᜻
ᦪᡠg(-x)ᓽᦪ“ᨵa(-x)1+(3a♦1)(-«)2♦(6*2)(-x)+bo-(ax1+(3a+1”'♦(b+2)z3c+1=0.6n0.a--y,i=0,Ḅ᪆⊤/U)--yxJ+Z(U)(I)g(*)=-+'+2x,ᡠC'(*)=-/+2,g'G)=0,஺=-"x,=஽■.ᑣ'x<-6ᡈx>஺*.g'(x)<0,g(Gᙠ,-(-8.-Tfj.♦8)012
ᦪ;'-&0.g(Qᙠ,-6-஽.ᦈ௃01ᵯ
ᦪ.ᵫ9☢;<©(*)ᙠ,>1.20ḄᨬᜧABᨬCADEᙠX=1F,2*G&প=f.fi(^)I,J2)=y.J᜜ᙠ,-”,2௃0ḄᨬᜧM|-N,ᨬCA2)-1.(2010ᦻᦪ)(21)("⚪$ᑖ15ᑖ)&'ᦪf(x)=(x-a)2(a-b)(a,beR,aᦪ?@A᳝,஽C3"14ᢥEFGH᣸ᑡKḄLMᦪᑡN(O(IM%஺-B|.ᦈS/'C)ᦑ/'ব->

33¾஻2)=0.ᡠ¼“ᙠH<2.0)ᜐḄᑗÃ(᫭y«4-2.(IIுÆÇ:ȸÉ=3(.a“xFf.ᦑa<-yvfRRKDḄᓽÌftÎHJÐ'ÑÒ\Óஹ=஺.ÔÕÖ.~A.11×.Ø4*)ḄÙH.ᦑ/£&,¾»2(6"Û.IÜ▲♦2&ஹ23•6tᓅh”.*3♦"¯”•&âãᡂE±ᑭᡠ¼åæçᦈ*.Øᙳᵯ.ë஽=í.(2010ᳮᦪ)(18)(⚪ᑖ13ᑖ,প25ᑖ"(II)28ᑖ)£.ᦪ/(x)=—~-+ln(x+l),ᐸ¦óᦪaH1«x+a(I)õa=-2,ö÷y=/(x)ᙠH(0,/(0))ᜐḄᑗ÷(ø¯(II)õ/(x)ᙠx=lᜐùG᩽"ú±²/(x)Ḅᓫឋ஺♦a-(2-1)]Q+1]0m(I)¸প=(x+a)2x+1(x+a)2+x+1,fa=2h,u(0)=(<

34(D)ᵫ(I)OP)=Q+$=T+*.Uᙠx=1ᜐG᩽Aᡠf'(l)=0,ᓽX77+#=0,a=-3.a412*Pᑗ=+ln(x+1),ᐸ[\](-1,3)U(3,+«),^Oভ=`+rh=♦þ/ᵫaভ=°”ಔ=7.'-1<%7*,/(*)>0#'1.ᡠfXx.-^~^~2.X€(O.+OO),e/'(2)=1.ᓽ)*y-/Cx)ᙠ+ᜐḄᑗ*f᳛S1.................:.............h/(?)=ln2+2.ᡠ)*y-/(x)ᙠ+(2./i2»ᜐḄᑗj.k5Sy-

35>0,eG)o,ᦔ஻zᓫa⌴{X(2)ᵫ/(*>-o,nnax*-x+1—a»0.~3Xi■■1.x*"——1.aX*4--j-Bt.x*-z>.ᨌ80ᡂ.e/3v*ᦔ/(*)ᙠ<0.+8>Ga⌴wτঝ0VaV"I".:1>1>0.r€<0,D,g">>0,e,ᦪG)ᓫ2⌴wXx6(1.஺-1).᜜VO.e/(>0,ᦪ/GO⍒τx€(7-1,48)BhzXAO.e<0.ᦪᵨ>a⌴w,ঞcV0ᵫL-IVO,a::=(0.1)o>>0,e/(x)<0,ᵫᦔ/(x)ᓫa⌴▲I*60,ᦪ/(x)ᓫa⌴.ᡠ<a40,ᦪ/G8ᙠi0,18ᓫa⌴wτᦪ/2)"#n2A=(%,&'…)')'B=(]^2,…bQeS”,*+A,BḄ/0A-B=(\a-b\,\a-b1,--la,,-b„l);}t22A,B56Ḅ780d(A,8)=Zla-/7,Iti-1(I)@n=5B'CA=(0,1,0,0,1),8=(1,1,1,0,0),DA-8,d(A,8)E(U)GH:XM,KCeS,'ᨵA—5eS“'Pd(A—C,8-C)=d(A,8);

36(Ill)GHQXM,8,CeS“,d(A,B),d(A,C),d(8,C)RSᦪTUVᨵWSXᏔᦪ(I)Z:A-B=(|O-1|,|1-1|,|O-1|,|O-O|,|1-O|)=(1,0,1,0,1)J(Afi)=|O-l|+|l-l|+|O-l|+|O-O|+|l-O|=3(II)GHQCA=஺“),8=(a/2,…⊈,),C=(C],Q,…,q,)eSne0f'-e{0,1},ᡠh.Wjk{0,1}(»=1,2m,஻)A—B—(|q-bjJ%—ᓽ,…I஺”S,ஹᵫ⚪tu,4,q€{0,1}(/=1,2,…@q=஺B,—x=yWᵨ@q=1B',W{|W,W°}=|(1_f)_(1_e)|=|fWᡠhd(A-C,8-C)=tW-bJ=d(A,8)/=1(HI)GHQCA=(q,ᵯ'…ᔩ),8=(4'…),C=(q,R,i,c,)€S”d(A,B)=k,d(A,C)=l,d(B,C)=h0=(0,0,…0)wS,ᵫ(H)d(A,B)=d(A-A,B-A)=d(0,B-A)=kd(A,C)=d(A-A,C—A)=d(0,C-A)=/d(B,C)=d(B-A,C-A)=hᡠh=1,2,•••,«)T1ḄSᦪ0k,|cE-a|(/=1,2,■■■,»)T1ḄSᦪ0/;CtX-41=kW=1ᡂḄjḄSᦪ஺ᑣ஻=/+%-2/ᵫ'/,/1RSᦪX᜻ᦪᓽd(A,B),d(A,C),d(B,C)RSᦪTUVᨵWSXᏔᦪ஺

37(2010ᓅᳮᦪ)(IS⚪ᐳ13ᑖ)ᦪ/8)=In(1+r)T2(I)@᝕=2B'D¡y=f8)ᙠ¤(1,f(D)ᜐḄᑗ¡¨©E஺)Dª«)Ḅᓫ®6஺,1ZQ(D@¯=2B'f(x)=ln(l+x)—x+x*,f'(x)=-----1+2x\+x3ᵫ#/(l)=ln2,/'(1)=-,ᡠh¡²=/(x)ᙠ¤(1,/(l))ᜐḄᑗ¡¨©03y-ln2=-(x-l)ᓽ3x-2y+21n2—3=0,ஹ´'ஹx(kx+k-1).,ஹ(II)f(x)=----------,XG(—l,+oo).1+Xx@·=0B'f\)=W_—.X1+xᡠh'ᙠ®6(W1,0)¸,/'(x)>0Eᙠ®6(0,+8)¸'/'(%)021W"1-kᡠh'ᙠ®6(W1,஺)Á(——,+8)¸'/'(x)>oEᙠ®6(0,ߟ-)±,/v)1B'/,(x)=x-x+D=0,»᳝(-1,0),x=0.21+xk

38l-k1-kᡠhÅᙠ®6(-1,)Á(0,+8)¸'/'(%)>0Eᙠ®6(•,0)¸'~k~/V)0PaHl),g(x)Xf(x)ḄÌᦪ.1-a(I)Cᐵ#xḄ¨©D----------=g(x)ᙠ®6Î2,6иᨵÑᦪZ'DfḄÒÓ(x-l)(l-x)ÕE஻2—n—n2(II)@a=e(e0Öᯠ"ᦪḄØᦪ)B'GHQ£g(k)>/Ek=2yj2n(n+l)(III)@0()y+iX—1ᦑg(x)=k)ga----Txe(—<=0,—1)U(1,+0°)X+1ᵫlog—E——------=log-~~-»u(2uX-1)(7-X)"X+1t=(X-1)2(7-X).[2,6]ᑣt=-3X2+18x-l5=-3(x-1)(x-5)ᑡ⊤᝞ÿX2(2,5)5(5,6)6t'+0-t5/᩽ᜧ3225ᡠ£1ஹḄ=5,L=32ᡠtḄ5,32.........................................5ᑖ

39n-1+ln஻+lJ23n-\=ᡭ(-x-x-xx-)----345஻+l=—ln----------21_-2]#஻(2)=—>/----=-2/nz+z—-,z>0zz2iiᑣU(Z)=---bld---=(1——)220ZZZᡠ஻(z)ᙠ(0,+8)2345ᦪcd'ef>1>0,ᡠ“(J᝝:)>"(1)=0஻(<+1)Q1---------ᓽ/஻-----------r2>0n(n+l)n(n+l)ᓽ£ᓰg(@ுy2]2gn(஻n+g\)"......(3)Cᑣp>l,1

40"44XY஻IIV£f(k)W0.2(I)pa=l,qrsyuf(x)ᙠv(2,f(2))ᜐḄᑗsyz{(II)pᙠ|}±,f(x)>0ឤᡂGqaḄ._22.ூ᪆௃de⚪⌕ὃrsḄᑗsyzஹᑭᵨᦪẆ5ᦪḄᓫឋ᩽ஹẠiGὃᑖḄ¡¢y£.gᑖ12ᑖ.3(I)Ea=lFGf(x)=x3---x2+1,f(2)=3{f'(x)=3%2-3x,f'(2)=6.ᡠ2rs¦f(x)ᙠv(2,f(2))ᜐḄᑗsyz=3=6(x-2),ᓽy=6x-9.(II)f'(x)=3஻x2-3x=3x(஻x-l).#f'(x)=0,¨x=0ᡈx='.aªᑖ«¬®¯¨-5

41(2)pa>2,ᑣ00,2ᓽ.8ExeFGf(x)>0¹º<22f(-)>0,1..-7>0.a2a2¯¨---1FG/(x)>g(x)(III)᝞Ì᳝஺,Ï/(Ð)=/(Ñ2),ÊË᳝+஽>2ூ᪆௃de⚪⌕ὃᦪḄÓᵨGᑭᵨᦪẆ5ᦪḄᓫឋ᩽ẠiGὃᵨ5ᦪ¡¢ᑖ᪆ÔÕ⚪ḄGgᑖ14ᑖ(I)f'(x)=(l-x)e-J(,#f'(x)=0,¨x=lEx³ᓄFGf'(x),f(x)Ḅ³ᓄ®᝞ª⊤X(-°0,1)1(h+oo)Ø(X)+0-

42f(X)᩽ᜧᡠf(x)ᙠ(-8,1)ᑁ345ᦪGᙠ(1,+8)ᑁ3Ú5ᦪ஺5ᦪf(x)ᙠx=lᜐ¨᩽ᜧf(l)ᨴe(II)ÊË:ᵫ⚪Ý¿ig(x)=f(2-x),¨g(x)=(2-x)ei#F(x)=f(x)-g(x),ᓽF(x)=xe~x+(x-2)ex~2º3F'(x)=(x-l)(e2A2-i)erExுlFG2x-2>0,XYe2x"-l>0,ße-*>0,ᡠF'(x)>0,XY5ᦪF(x)ᙠl,+8)345ᦪ஺XF(l)=e'-e1=0,ᡠxுlFGᨵF(x)>F(l)=0,ᓽf(x)>g(x).Ill)ÊË(1)p(X1-1)(Ñ2-1)=0,ᵫ(I)f(X)=f&2),ᑣ%=à2=1Xáâ஺(2)p(X1-1)(ã2-1)>0,ᵫ(I)f(X)=f(X?)G¨᳝=஽.ä஺/áâ஺᪷æ(1)(2)¨(ᓰߟ1)*2-1)<஺GèCX<1GZ>Lᵫ(H)¿iGf|)>g&2),ᑣg&2)=f(2-X2),ᡠf&2)>f(2-X2),XYf(xJ>f(2-X2),°஽>1Gᡠ2—/<1Gßᵫ(I)¿i5ᦪf(x)ᙠ|}(-8,1)ᑁê45ᦪ,ᡠ᳝>2—%Gᓽ᳝+ã2>2.(2010ëìᦻᦪ)22.(de⚪gᑖ14ᑖ)hi5ᦪf(X)-d+ax+bḄÄíᙠvpᜐḄᑗsyzy=3x-2(0{f(0))3(I)qîᦪa,bḄ{(II)Cg(x)=£&)+-32,+82Ḅ45ᦪ஺X—1(I)qîᦪmḄᨬᜧ{

43(ii)EmᨬᜧFG3ᔲòᙠvQ,ó¨ôvQḄÇsprsy=g(x)ᡂ«õö÷ÄøGᑣù«õö÷ÄøḄ☢û_ü?pòᙠGqývQḄᙶ᪗
ᙠᳮᵫ஺22.⚪⌕ὃᦪஹᦪẠ,ὃᳮ!"#ஹ$%᠘'Ḅ#ஹ)*+,"#-ᦪ.ᔊ012ஹᦪ34ᔠ12ஹᓄ7.8ᓄ12ஹᑖ:.᦮ᔠ12.<ᑖ14ᑖ.,?@A,f/'(0)=3.fa=3,(Dᵫ/'(x)=J-2x+oN⚪PRஹᓽUஹ/(0)=-2.[b=-2.(n(i)hg(x)=-x3-x2+3x-2+-^-t3x-1Rg\x)=x2-2x-r3-(ஹ

44ᓽ-2x+3——J>0/|[2.+00)`nᡂo.(>-1)2P(XT-=t,/xe[2,-wo)...te[l.+x),ᓽtuf+2-/•2஺ᙠ[l.+oo)`vᡂজ,xvS0z,P{=r+2—'20ᙠ[1|8)HHᡂo.tm>0Hl.Py=r+2-',rw+xl/=1+2>0,ᡠᦪ{=r+2-'ᙠ[l>xM-ড.rt௃=3-v.01a>0..3—ni>0,ᓽm<3ᑗ>0,ᦑ0

45
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50(201045ᳮᦪ)(22)(8⚪9ᑖ14ᑖ)1Q;*<ᦪ/(x)=+------\(aeR).x(1)=஺>(?+@A/(X)ḄᓫCឋE(II)Fg(x)=--2bx+4.=?+GHIX|W(0,2),JᙠL26,M/(xJ?g(X2)NOᦪ஻QRT.ூ,᪆௃(I)X<ᦪḄYZ[!(0,+8),\!/(x)=l1-a_-ax2-h:+a-l+ᡠ/X=a=0?+/5)=]+^/(x)=T>0-x>Lᡠ/XX_?<ᦪf(x)ᙠ(1,+8)abc<ᦪEᙠS+1)abe<ᦪ:121a11/1/x-2XX-^+21-X2+2X-1=j?+/(X)=-----2j~--=----2-=---LX0ᡠ/2x2x2x_?<ᦪf(X)ᙠ(0,l8)bm0--axf-l+a>0,,-x>lᡈx3+a)>0--ax'tu+a>0+,-l0--ax2~h:-1+a>0,,-_?<ᦪ2xaf(x)ᙠabc<ᦪEᙠ(0,1-1)v(1,+8)abe<ᦪEaa=a21?+ᵫyL1V0,^/(x)=*°+a,>0--axF-l+a>0,),-0

51ᨵf(xj?f(l)=-,´IJµᙠ஽€[,2],º/(X1)2g(X2),ᡠ;g(X2)Xe[\,2],29ᓽµᙠxw[1,2],g(x)=x2-2bx+4<——,ᓽ2bx?*2+2,ᓽ2b2x+2e[U,U],22x24ᡠ¿À6ᓽxᦪbA/C[U,+8)஺244ூÂ⚪ÃÄ௃⚪ÆÇᦪஹÈᦪஹ>É|JÊᨵËḄÌᔠᙠÎὃÐᑭᵨÇᦪẆÔᦪḄᓫÕឋஹᑭᵨÇᦪ@ᦪḄᨬ/0ÈᦪḄᨬ/Ø⚪ὃÐ?ÙÚᑖÛÜÝḄᦪÙÞß0¿>É|ḄàὃÐÙáᔠâᵨᡠÙJÊᑖ᪆Ø⚪ஹ¿gØ⚪Ḅà஺(1)äåᑭᵨᦪæÇᦪḄᐵçÜÝᦪḄᓫÕឋ(2)ᑭᵨÇᦪ@t/(x)Ḅᨬ/ஹᑭᵨÈᦪJÊᡈᑖéêᦪë@tg(x)ᙠìíî[1,2]Ḅᨬᜧ/ᯠñ¿>É|@òᦪ஺(2010ᓭᳮᦪ)20.(⚪ᑖ13ᑖ)IJᦪ/(x)=x2+bx+c("ceR),øùÃḄxeR,ឤᨵf(x)W/(x)஺(I)346x?07/(x)<(x+c)2(II)8øû⚪ᩩüḄùÃb,c,>É|/(஺)/S)þJ(/-/)ឤᡂ
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55(2010Eᓅᳮᦪ)21.(⚪ᑖ14ᑖ)!"#ᦪf(x)=ax+-+c(a>0)Ḅ%&ᙠ(l,f(1))ᜐḄᑗ*+,-y=x-LX(I)ᵨa⊤01b,c+(n)2f(x)21nxᙠT1,+8)3ឤᡂ67⌮)9:<=(III)>?)+A+1+…+1>ln(n+l)+Vஹ(n21)23n2(n+l)21.SSB⌕ὃIf#ᦪஹ•FᦱஹHIḄ>?J?LM"N.ᔣQὃRSᔠUᵨᦪV"WXYZᳮ\>Ḅ]^_ᑖ`\Ḅab.cᑖ14ᑖ)dJ<1)eḄ”-h,ᑣY*dெmJ-JxJnmo)=°-0=1.k=l-2d(II)ᵫ(ூ)",/(x)■ax♦-~-+1-2a.xgM=/(x)-Inx=zzr+-----+௃-2a-௃nx,XGI.XO)xo-11a?-->o(x-Wr-l)Mg(l)=0.gXx)=auVMV9.ᑣg'(x)vO.K(x)ᜐvḄᦪ,ᡠx8(x)v8(l)=0,CP/(x)l.W^f(x)>0.g(x)yz{ᦪᡠxg(x)>gপ=0,KP/(x)>lnx.ᦑQ/(x)ilnx.|3ᡠ},ᡠᩭ஺Ḅ9:-g,y>).(2010WXᳮᦪ)17ஹ(YZ⚪\ᑖ12ᑖ)^a:_ᦪ`ᦪ/(x)=e'-2X+2Q,XWR஺

56(I)a“X)Ḅᓫ589᩽d+(H)af?a>ln2-lgh>0&ex>x2-2ax+1»(17)(YZ⚪\ᑖ12ᑖ)Y⚪ὃklᦪḄmnᑭᵨlᦪẆr`ᦪḄᓫ589a`ᦪḄ᩽dᙳft`ᦪuvw,ὃkmnxyஹzᔠᑖ᪆${|⚪Ḅxy.(I)?ᵫ/(x)=e-2x+2a,xWR~/'()=e'-2,x6R./'()=0,♦x=h»2.zᓄ&J'(x).Hx)Ḅᓄ᝞ᜱ:X(-00fIn2)In2(R2.♦x)Z)-0+ᓫ*⌴,ᓫ-⌴.Z)2(1-!n2+a)ᦑ/()Ḅᓫ⌴=89(ln2),ᓫ5⌴789(ln2,+x),/tx)ᙠx=ln?ᜐ᩽Zd,᩽Zd:/(ln2)=ehl-2ln2+2a=2(1-In2+a).(H)f?^wx)=e'Cax-l,xeR,(x)=e'-2x+2a,x6R.ᵫ(1)~”!n2-l&,g'G)ᨬZd:g'(ln2)=2(1-ln2+a)>0.xWR.ᨵg'(x)>0,ᡠ⇟x)ᙠRᑁᓫ5⌴7.a>In2-1&.(0,+«),ᨵg(x)>g(0).g(0)=0,xW(0,+8),w)>0.ᓽ/-x?+2ar->0,e>>¡-2ax+L(2010¢£ᔁ)20ஹ(YZ⚪\ᑖ16ᑖ)^/(x)¥¦ᙠ89(1,+8)§Ḅ`ᦪᐸl`ᦪ:'(X)஺᝞©ªᙠ_ᦪa$`ᦪ/z(x),ᐸ¬h)Ḅxe—ᨵh(x)>0,®/'(x)=h{x}{x2-ax+\),ᑣ°`ᦪ/(x)ᐹᨵឋ³P(a)஺প^`ᦪ/(x)=lnx+——(x>1),ᐸ¬ᓃ:_ᦪ஺x+1পaf?`ᦪ(X)ᐹᨵឋ³P3)+(ii)a`ᦪ/(X)Ḅᓫ589஺(2)·~`ᦪg(x)ᐹᨵឋ³?(2)஺¹¥º(1,+8),᳝l,᜛>1,i2t2½Ig(a)-g(᜛)l

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58ñ஻(X)ḄXW(1,+8)ᨵ//(x)>0,ᡠḄXW(1,+8)ᨵg'(x)>0,g(x)ᙠ(1,+8)§⌴7஺ña+஺=X[+x,a-=(2ó-1)(ᓰ஽)஺2"÷>+,஻2Hl&ag(a)-gGff)>g(Xx)-g(x)ᔠ⚪.x2X1,506_82=m(4-XU-<=-x?),=ᳮᨵ@<£0,0("ீD0"E+(l-m)x<஽22GᔠHIJK0*6ᡠMNḄPQST(0,1)஺(VWX)ᵫ⚪Z[,g(x)Ḅ\]ᦪg'(x)=//(x)(x2—2X+1),ᐸb]ᦪc(ᵫ>0defḄXW(1,+8)iᡂk஺ᡠH0+x>l/0g'(x)=஻(x)(x-l)2>0,mng(x)ᙠpq(1,+8)Iᓫs⌴u஺জ+me(0,1)/0ᨵa=mx+(1-//J)X>mx+(1-m')x-᳝0t2[la-mx+(1-m)x

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