函数与导数高考真题练

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ᦪᦪὃ⚪1ஹ(⚪ᑖ12ᑖ)2016ᐰᦪ/(%)=(-2)er+a(x-l)2প!"f(x)Ḅᓫ%ឋ'(H))/(x)ᨵ,-./01஺Ḅ346஺7᪆9(I)f(x)-(x-+2a(x-1)=(x-l)(ev+2a)প@a20A0@xe(-8,1)A0f(x)<0,@xe(l,+8)A0f\x)>0,•••/(x)ᙠ(-oo,l)ᓫ%⌴J0/(x)ᙠ(1,+8)ᓫ%⌴KফMa<0,ᑣ/(X)=0Px=1ᡈx=ln(-2a)জ)஺=TU,ᑣf(x)=(x-l)(e*-e),ᡠX/(x)ᙠ(-,+-)ᓫ%⌴K'ঝ)஺>TU,ᑣln(—2a)09@xe(ln(-2a),l)A0/,(x)<0'ᡠX/(%)ᙠ(ߟ_ln(—2a)`(1,+8)ᓫ%⌴K'ᙠ(ln(-2a),1)ᓫ%⌴J஺ঞ)ac-1,ᑣln(—2a)>l,ᦑ@xw(-oo,l)U(ln(-2a),+8)de0/()>09x@xe(l,ln(-2a))A0/(%)<0'ᡠX/(%)ᙠ(—,1)`(ln(—2a),+8)ᓫ%⌴K'ᙠ(lfn(-2a))ᓫ%⌴J஺(H)প@a>0A0ᑣপ/(x)ᙠ(—8,1)ᓫ%⌴J0ᙠ(1,+8)ᓫ%⌴K0g/(1)=—e,/(2)=a,3hih<0jk|(o-2)+஺(஺-1)2=a(b2-h)>0,ᡠXf{x}ᨵ,-./ফMa=0,ᑣ/(x)=(x-2)/,ᡠX/(x)ᨵT-./বM஺<0,)a20,ᑣᵫপf(x)ᙠ(1,+8)ᓫ%⌴K,g@xWlA0/(%)<0,ᡠ2X/(%)stᙠ,-./')ᑣᵫপ/O)ᙠ(1,3—2a))ᓫ%⌴J0

1(ln(—2a),+8)ᓫ%⌴K0g@xW1A0/(x)<0,ᡠX/(wstᙠ,-./;yz0஺Ḅ346{(0,+8)2ஹ(⚪ᑖ12ᑖ)2016ᐰ11|}ᦪ/(x)=(%+1)Inx-a{x-1).(I)@a=4A01y=/(x)ᙠ(1,/প)ᜐḄᑗo;(II))@xe(l,+8)A0/(x)>0,1aḄ346.7᪆9(I)/(wḄ(0,+8),@a=4A0/(x)=(x+l)lnx-4(x-l),f\x)=

2x+3,/(1)=0,/(I)=0,xy=/(X)ᙠ(1,7(1))ᜐḄᑗo2x+y-2=0'(II)@xe(l,+°°)A0/'(x)>0q~->0x+1tz(x-l)12ax~+2(1—ci)x+1Mg(x)=lnx-ᑣg(x)=T—1)=00x+1X(x+l>x(x+l)2প@aW2,xe(l,+8)A0%2+2(l-tz)x+l>x2-2x+l>0,ᦑg(x)>0,g(x)ᙠ(l,+8)zᓫ%⌴K0ᡠXg(x)>0'ফ@a>2A0g(x)-0=%|=a—]—J(a-1)--10—1+-1)--1ᵫ2>1`᳝2=1P<10ᦑ@€(1,஽)A0g'(x)<0,g(x)ᙠ(1,)zᓫ%⌴J0Ag(x)

3Mᦪ/(x)=lnx-x+lপ!"(wḄᓫ%ឋ'(II)@xe(1,+8)A01<^~-l,@ᑍ£(0,1)A0l+(c—l)x>F7᪆9(1)/(wḄ(0,+8),/(x)=--l,f(x)=0nx=l,X@0cx<1A/(¤)>0,@ᑍ>1A0/(x)<0ᡠX/(wᙠ(0,1)ᓫ%⌴K0ᙠ(1,T)ᓫ%⌴J0(H)ᵫপ/(x)ᙠ=1A3Pᨬᜧ40ᨬᜧ4/(1)=0@¤¤1Aஹlnxl,Mg(x)=l+(஺-1)¤T᮱0ᑣg(x)=c-l—c"lnx1C-lhIn-"g'(x)=0=>JC=—0Inc@xo0g(x)ᓫ%⌴K'@x>XoA0g'(x)<00g(x)ᓫ%⌴J;ᵫ(II)ᦑ00,IncᡠX@(0,1)A0l+(c-l)x>c*4.(⚪ᑖ12ᑖ)2017ᐰᦪ/(x)=e'v(ex-a)-ax.(1)!")(x)Ḅᓫ%ឋ'(2))/(x)20,1஻Ḅ346.ூ®ᫀ௃(1)@a=(),/(X)ᙠ(—8,+8)ᓫ%⌴K'@஺±0,/(x)ᙠ(—8,]na)ᓫ%⌴

4J0ᙠ஺”+8)ᓫ%⌴K'@"0,)ᙠfl"))ᓫ%⌴J0ᙠ(³´0+8)ᓫ3%⌴K'(2)[-ூ7᪆௃¶⚪ᑖ᪆9(1)ᑖ4=0,஺ு0,4<0ᑖ¸!"ᦪ/(X)Ḅᓫ%ឋ'(2)ᑖ4=0,஺ு0,a<0ᑖ¸7/(x)>0,¹º»aḄ346.¶⚪7᪆9(1)ᦪf(X)Ḅ(-8,+8),f\x)=2elx-aex-a2=(2"+a)(e'-a)জ)a=0,ᑣ஻x)=e2*,ᙠ(-8,+8)ᓫ%⌴K.ঝ)aு()0ᑣᵫ/'(x)=0Px=Ina.@xe(-8,lna)0e0f\x)<0'@xw(In஺,—)A0f\x)>0,ᡠX/(x)ᙠ(-8,lna)ᓫ%⌴J0ᙠ(Ina,+8)ᓫ%⌴K.ঞ)a<0,ᑣᵫ/'(x)=0Px=ln(-]).@xe(-8/n(-g)A0f\x)<0'@xe(³T¼,+8)A0f\x)>0,ᦑ/(x)ᙠ(—8,ln(—½))ᓫ%⌴J0ᙠ(ln(—@),+8)ᓫ%⌴K.22

5(2)জ
a=0,ᑣ/(x)=/3ᡠ/(x)NO.ঝ
஺>0,ᑣᵫ(1)x=lnaf(x)ᨬᨬ/Qna)=—/Ina.-a1Ina>0,ᓽa41,f(x)>0.ঞ
a<0,ᑣᵫ(D,x=ln(-£)/(x)ᨬᨬ/(ln(-g))=a--ব2242-3a-d[--ln(--)]20,ᓽa2-2e0/(x)>0.42aḄ![#2)$].ூὃ)௃+ᦪ-ᵨூ/0)1௃2⚪4⌕ὃ6+ᦪḄ7ᜧ9☢Ḅ-ᵨ;(#)>ᦪᓫ@ឋḄBC;Dᵨ+ᦪEFᩭBC>ᦪᓫ@ឋHᐜὃ⇋>ᦪḄKLMNOPQ'(X),ᨵ/'(X)ḄUVP>ᦪ/(x)Ḅᓫ@WXY(Z)>ᦪḄᨬ(᩽)ḄO\;ᵫ]^Ḅᓫ@WX_ᔠ᩽)ḄKLabcdḄ!P>ᦪ/(x)᩽ᡈᨬ.20.(2016ÃÄ)(⚪ᑖ15ᑖ)Mᦪ/(x)=x3+fT0xe[0,l].91+x(I)/(x)>1-x+x2;33(ID-

6ᵫgxe[O$],ᨵgpi-x+x2-^<—,1+x1+x1+xᡠ/(x)Nl-x+f.(H)ᵫOSxWl/Vx,1,133(x-l)(2x+l)3,3ᦑ/(x)=f+--VxH-----+-=---9--9--+-V-1+x1+x222(x+l)223ᡠ/ëxìW'.ᵫi1ì/iᑗk1#l+/=Yo#:Y+qkr,st/u/ᔁுr,ᡠxಘzὃ/9ᦪḄᓫ%ឋᨬ4ஹᑖËᦪ.