2023年高考数学大招2导数构造秒解大法

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⌱⚪Ḅ⚪ᦪḄ᪀⌼⚪᝞᪀⌼ᦪ!"ᵨ$%&'(.*+,᎛᝞./ᦪ᪀⌼ᜧ01234567(&ᡧ9.ᦪ᪀⌼ᜧ:▭<=>᪀⌼ᡈὅ$AB᪀⌼CD᪷FᦪGH“JK”ᦪᓫNឋ.P&'Q('(X)R☢ḄGH᝞.>“>”ᑣVW᪀⌼ᦪXY᝞.>“<”ᑣVW᪀⌼ᦪXᡄ.P\'Q]H^Ḅ_ᦪ⚪`a&+_ᦪᐸcdḄᦪe0af*+_ᦪgᐭi⚪jkllmGᔠ.Po'CD3pᫀ.᝞./'(X)R☢ḄGH>ᑣpᫀri⚪sHtuvwx&yjk>_ᦪ᝞./'(X)R☢ḄGH>“<”ᑣpᫀri⚪{Hs᪵vwx&yjk>_ᦪ.᝞.ᨵ~⚪`ᨵa_ᦪt>CDvw᝞/(x+l)>(x-l)/(x2-1)ḄᑣCD᪷Fᡃ“JK”ḄᓫNឋ]HᑁḄᜧᓽᵨᦪ☢Ḅᦪ.&%Ḅ>ᓫᩭᦢḄ⚪`ᑖ=¡R=5&⍝⚪(.>ᨵ&kḄ¤▲ឋ⍗ᑮk¨©Xªᦪᡈ«¬ᦪ᜻Ꮤឋ6ᡈ⌱⚗^ᨵm+GᔠḄ,᎛=ᨵ°ᜫᦔ.³ὅ&C23>´ᙠ◍Ḅᡠ¸¹ᜧº»¼(ᙠ:ᙠḄ½%ᡈὅὃ,¿ÀÁḄ,᎛ÂÃᵨ.%☢ᡃ=&ÄᩭQQ⍝⚪"Å&%cḄ(.ᐺÇ⚪1k¨ᙠR<Ḅᦪ/(x)ÈÉÊ/(%)+f'(x)>1,/(0)=4ᑣvweV(x)>ev+3(ᐸ^eXÏᯠcᦪḄÑᦪ)ḄÒX()A.(0,+oo)B.(-,0)U(3,+oo)C.(Y»,0)50,+8)D.(3,+oo)

1Ê1"Óg(x)=e"(x)—",(XGR),ᑣg'(x)=e"(x)+exf'(x)~e*=ex[f{x)+/r(x)-l],•■•/(x)+r(x)>l,.■,/(x)+r(x)-l>0.••.g,(x)>Ot•.y=g(x)ᙠk¨©<ᓫN⌴Y1•,exf(x)>ex+3.g(x)>3,Xv^(0)=e°/(0)-e°=4-1=3,#g(x)>g(0)#x>0.ᦑ⌱A.2"f(x)+f'(x)>l,*Ö>ᡠpᫀre"(x)>e*+3sH,Øxf'(x),u/(2)=4,ᑣvw/(x)—2x>0ḄÒX()A.(2,+oo)B.(0,2)C.(0,4)D,(4,+oo)Ê1"Óg(x)=/H,ᑣg#(x)=Ú'(x)Ê/(x),XXf(x)>xf'(x),g'(x)<0,ᓽÝQ0,ᦪg(x)ᓫN⌴Þ"/(2)=4,••.g(2)=/?=2,ᑣvwfM-2x>0vßXg(x)>gফ#ᓽ()0.ᦑ⌱B.2"/(%)>xf'(x),ᐜá⚗xf'(x)-â)<0,*Ö>“<”ᡠpᫀr/(x)-2x>0{HØ2ḄÒX()

2A.(-oo,0)B.(0,+oo)C.(-oo,2)D.(2,+oo)ÊèÓg(x)=9,ᑣ/(9.•••/(X)0,ᓽᦪg(x)ᓫN⌴Y.•.*0)=2,••.g(O)=*=/(O)=2,ᑣvwê஺>2vßXᓽg(x)>g(஺)exexe•.•ᦪg(x)ᓫN⌴Y.••x>0,vw/ì>2ḄÒX(0,+8).ᦑ⌱B.ex2:/(x)0,*Ö>“>"ᡠpᫀrê»>2sHØ2,ðlJ/(x)>2x+4ḄÒX()A.(-1,+oo)B.C.(2,+oo)D.(-oo,-2)Ê1ÊÓæ(x)=/(x)—(2x+4),ᑣæ(-1)=/(&1)&(-2+4)=2—2=0,6cîïxeR,f'(x)>2,ᡠF(x)=/'(x)—2>0,ᓽE(x)ᙠR<ᓫN⌴Yᑣæ(x)>0ḄÒX(ߟ1,+8),ᓽ/(x)>2x+4ḄÒX(-1,+00).ᦑ⌱A.2"/'(x)>2,*Ö>“>"#ᡠpᫀr/(x)>2x+4sHØ

3vw/(%+1)>*-1)/(&&1)ḄÒ>()A.(0,1)B,(l,+oo)C.(1,2)D,(2,+oo)Ê1"Óg(x)=xf(x),ᑣg#(x)=[j/(x)]z=x'f(x)+xf'(x)=xf\x)+f(x)<0,ᦪg(x)ᙠ(0,+8)<>Þᦪ••1/(x+l)>(x-l)/(x2-l),XG(0,+oo),•••(X+l)/(x+1)>(x+l)(x-l)/(x2-1).(x+l)f(x+1)>(x2-l)/(x2-1),g((+l)>g(x2-r.x+lvf-1,3x>2.ᦑ⌱D.2"f(x)<-xf\x),ᐜá⚗,xf(x)+f(x)<0,*Ö>'■<1',ᡠ᪀⌼ᦪX⌴Þ»◤⌕/0+1)>(õ&1)/*2-1)]HᑁḄᜧᓽᓽ1+1<%2&1Â"03x>2.ᦑ⌱D.x2-l>06.ãäᦪy=/(x)cîïḄxeRÈÉ2"'(x)-2"(x)ln2>0(ᐸ^æ(x)>ᦪ/(x)Ḅᦪ)ᑣ%ᑡvwᡂúḄ>()A.2/(-2)/(2)C.4/(-2)>/(0)D.2/(0)>/(1)f(\#/ஹ2"'(ü—2"ln2"x)xÊ1"᪀⌼ᦪg(x)=/^2ᑣg(x)=.(2#)&.xeRÈÉ2xf'(x)~2*/(x)ln2>0,g#W>0,ᓽᦪg(x)ᙠR<ᓫN⌴YðIJg(—2)

4ᓽ2/(-2)0,Ḅ◤⌕᪀⌼Ḅᦪᦪ◤⌕ᑁḄᜧᓽ.••2<—1,#A!".#7.$%/(%)R*Ḅ+ᦪ,-./xeR,ᙳᨵ/(x)>f\x),ᑣ456!"Ḅ()A,e”(-2017)/(0),/(2017)<^0,7/(0)D.^'7(-2017)>/(0),/(2017)>e20,7(0)718F(x)=42ᑣF()=[4^]=9/®x:/(x)>r(x),ᡠ49(x)<0,ᡠ4<(X)=ᦪ:2017<0,2017>0,ᡠ4<(-2017)><(0),<(2017)<1(0),ᓽᡠ4*'7/(2017)>/(0)=,>|7)<,ᓽ/(2017)/'(x),_f(x)-/(x)<0,Ḅ◤⌕᪀⌼Ḅᦪ=ᦪ◤⌕ᑁḄᜧᓽ.••--2017<0,2017/(-2017)>/(0),•■-2017>0,A/(2017)

5C.10)D.(10,+w)7M1"᪀⌼ᦪg(x)=/(x)—X,ᑣᦪḄ+ᦪg'(x)=/'(x)—1,Vr(x)1,ᑣDEF/(lg2x)i,ᑣigx>iᡈigx<-i,7Wx>ioᡈOl,ᑣlgx>lᡈ7Wx>10ᡈ00,(Z+1)/'(2஻(*)<0,ᑣDEF/(x)>0Ḅ7K()A.(i,+8)B.y,-i)c.(1)50,1)D.(—1,0)51,+8)f()"\(^+1)#'(_)-2a_)x7M1M᪷c⚪/8g(x)=4i,ᐸ+ᦪgW=-——-------')x2+l(_+1)fᵫYx>()(V+lJra)—21(x)<0,ᑣᨵg'(x)<0,ᓽᦪg(x)ᙠ(0,+8)*=ᦪfᵫᦪ/(x)᜻ᦪS=;—?—iߟ7=-g(x)#(-%)+1%+1

6ᓽᦪg(x)᜻ᦪᑣᦪg(x)ᙠ(0,+8)*=ᦪfᵫ/(-1)=0,SIJ/(1)=O,ᑣg6=g(-1)=0,ᑣᨵᙠ(8,-1)*g(x)>o,ᙠ(1,0)*g(x)<0,ᙠ(0ᙠ*g(x)>0,ᙠ(1,+8)*g(x)<0.Qg(x)>0,ᓽ4>0,x2+lᑣᨵy(x)>o,ᑣDEF”஺>0Ḅ7K(YO,T)50,D.ᦑ⌱c.2"Yx>0(f+i)r(x)—2W(x)<0#“<"ᡠ4Yxு0/(x)ᓫO⌴q.᝞sᦑ⌱C.#10.$%ᦪ/(x+2)Ꮤᦪ,Y_>2@Au(x)>2/'(x)+/(x),ᑣ()A.2/(1)஻3)C./(O)<4/^D./(1)2r(x)+f(x),W(x-/(x)>0,8/x)=yᑣ"a)''")."MM{J)V(x-2)/,(%)-/(x)>0,.•.YX>2஻'(x)>o,ᦪᓫO⌴.•••/(x+2)Ꮤᦪ/(x+2)ᐵ}~=0-ᓽ/(x)ᐵ}~=2-ᓽ/(D=/(3),ᦑD┯,

7(I)#/(0)=/(4),ᑣNᓽ4-2521ᑣ/(4)ு4/)ᓽ/(0)ு4/)ᦑC┯ᦑ⌱A.2"•/(x+2)Ꮤᦪ./(x)ᐵ}x=2-Y>2xf'(x)>2f\x)+f(x),(%-2)/7%)-/(x)>0,/(x)ᓫO⌴ᡠ42,ᦪᦑ⌱A.5☢⍝#⚪ᜧᜧᨵᜫᦔḄᱯY~<()Ḅ"ᨵᨵ¡ᑖ⚪£D¤ᔠᜧ¦£ᨬ¨ᢥ¡ª«ᜐᳮ.#11-}R*+Ḅ./ᦪ/(%)Q@A#)+4(x)>0,{-1)=0,ᑣ/(%)>07K()A.(-oo,-l)B.(0,+oo)C.(^o,-l)U(0,+oo)D.(-1,0)7M®g(x)=#(x),SIJg'(x)=/(x)+4'(x)>0,ᦪg(x)=4Xx)ᓫOᦪ,f/(-1)=0,•,"(-1)=(-1)/(-1)=0.ᑣYx<—1,W)<0,f(x)>0?Yl0,/(x)<0;Yx>0xf(x)>0,/(x)>0;•••/஺)>07K(-8,-1)஺(0,+8).ᦑ⌱C.

8#12.8ᦪ/(%)¯°ᙠ(-oo,0)*Ḅ+ᦪᐸ+ᦪf'(x),,ᨵxf'(x)>x2+2f(x),ᑣDEF4/(x+2014)-(x+2014)7(-2)>0Ḅ7K()A.(-oo,-2012)B.(-2012,0)C.(J,-2()16)D.(-2016,0)7:ᵫxf'(x)>x2+2/(x),(x<0),x2f'(x)-2xf(x)0EUF(x+2014)-F(-2)>0,F(x)ᙠ(ߟ8,())=ᦪᵫF(x+2()14)>F(—2)Wjr+2014<-2,ᓽx<—2016,ᦑ⌱C.#13.$%¯°ᙠR*Ḅ+ᦪ/(x),-}./¶ᦪx·ᨵ/(-B=/஺)-2%ᡂ¹,,YXG(-8,0U·ᨵ/'(x)<2x+lᡂ¹Q/(2º)

9D.-i,oo+I37M®g(x)=/(x)-/X,ᑣg(-X)—g(X)=/(-X)-x2+x-/(x)+x2+x=o,•••g(-x)=g(x),.•.ᦪg(x)R*ḄᏔᦪ.•Yxe(-8,0U·ᨵr(x)<2x+lᡂQ/(2¼)

10A.(-2,+00)B.(0,+oo)C.(l,+oo)D.(4,+oo)7M1
᪀⌼ᦪ8஺)=ÆeᑣᦪḄ+ᦪg3=ra)"7(x)e1.((B<7*),..,g(%)<0(e?ᓽg(x)ᙠR*ᓫO⌴=?fV/(0)=2,.\g(0)=Ç=2,ᑣDEF/(%)-2ev<0ᓄeY<2,eÈEU}g(x)<2,ᓽg(µ)(),ᓽᡠÉDEFḄ7K(0,+8).ᦑ⌱8.2"r(x)

11,g(-D=/(-D+l-2016=2015+1-2016=0,ᦑDEFf(x)eஹ+lḄ7K()A.{x|x>0}B.{x|x<0}C.{x|x<-l,ᡈx>1}D.{x|x<-l,ᡈ0l,•••g'(x)>0ឤᡂ¹ᓽg(x)=e"(x)-e'ᙠR*ᦪf"/(0)=2,:.g(0)=1,ᦑg(x)=e"(x)-e'>lḄ7K{x|x>0},ᓽDEFev/(x)>ev+1Ḅ7K{x|x>0}.ᦑ⌱A.4.$%/(X)Ḅ¯°×(0,+8)J'(x)/(x)Ḅ+ᦪ,@A(X)(Ý(x),ᑣDEF/(W+1)>(«-1)/(J1)Ḅ7K()A.(0,4)B.(1,4)C.(l,+oo)D.(4,+oo)7:8g(x)=7(X),ᑣg'(x)=[v(x)]x=7'(X)+f(x)<0,ᓽYx>0ᦪ

12g(x)=xf{x)ᓫO⌴=f(\x+1)>(y/x(Vx+l)/(x/x+1)>(x-l)/(x-l),.-.g(«+1)>g(x-1)9x-1>0v,7WMx>4,ᑣDEFḄ7K(4,+8),ᦑ⌱D.>/x+lásB./(1)>2/WsinlcমCM?)Dá(ãä)7M:x,ᡠ4sinx>0,cosx>0.ᵫf(x)0,®gsinxI2Jr(x)sinx-/(x)cosxí•ån\.xDফæ"ï”"’A.A!
ïu|un,—11-4H>òḄফᨔè"{Mj53/.2r(=sinxsinxv27/(;)ó;)}A#ᵫ}gᵪ7s'ᓽ\J—,.71.71sin—sin—43ᵫ}g(D>g஺à,ᓽõுভᓄêᓽᑨì8!ᓄêᓽᑨìA┯?-}8.16=sml÷

13\71\[71rrgøᓽ"?-}c,ᵫ}ᓄêᓽᑨìC┯?-}஺,.7C.71sinsin64ᵫ}g|aTg(M7tஹ6(5).ᦑO┯.ᦑ⌱,ᓽsin—sin—632B.6.¯°ᙠR*Ḅᦪ/(x)@AMr(x)>/(x)ឤᡂ¹Q᳝<஽ᑣ᮱"(%2)Ñe*2/(xjḄᜧᐵü()A.ev'/(x)>eJf2/(x)21B.eV|/(x)ejr2/(x).ᦑ⌱A.2l7.ᦪ/(%)ᙠRḄᏔᦪf'(x)ᐸ!ᦪ.#x>0$/(%)+&ব>0,)/প=0,ᑣ-./0ব>0Ḅ12()A.(ߟco,-1)(1,+cc)B.(-*51)5(),1)c.(-1,0)50,1)D.(-l,0)u(l,+o>)

141••(4XX))'=/(X)+J/'(X)>0,ᦑᦪg(x)=j/(x)ᙠ(0,+஺஺)ᓫ⌴.7᪷9ᦪ/(:)ᙠRḄᏔᦪ;<ᦪg(x)=4(x)RḄ᜻ᦪᦑᦪg(x)=4(x)RḄ᜻ᦪᦑᦪg(x)==vf(x)ᙠ(58,0)ᓫ⌴.>J\r/°yx/(1)=0,;./(-1)=0,ᦑᦪy=0Xx)Ḅᓫឋ᝞ABᡠD.ᵫ-./F'(H>°;஺Ḅ12(T,0)5L+8).ᦑ⌱D.8.PQᦪy=/(x)ᙠRḄ᜻ᦪ)Rব5/(x)>0(ᐸS/'(x)/(x)Ḅ!ᦪ)ឤᡂV.W“=d(=3)/=d(=2)4,=_Z(]),ᑣa,8,cḄᜧ]ᐵ_()A.a>b>cB.c>a>hC.c>b>aD.a>c>h1`/z(x)=£gᑣ/(x)=r஺g'gabḄxwRcᨵe(x)>XXf(x)ᡂV,•••/Xinx)>/(Inx).h\x)>0,h{x)ᙠ(0,+oo)ᓫ⌴.•••/?(1)b>c.eᦑ⌱A.9.PQᙠ(F,0)Ḅᦪ/(x),ᐸ!ᦪh/'(x),W2஻x)—[(*)>0ᡂV,X+1

15ᑣiᑡLkḄ()A./(-e)-e2/(-D>0C.e2/(-e)-/(-D>0D.e4/(-e)-/>01..2f(x)-xf'(x),_$2/(x)—V'(x)<0.—lQx<1x+12/(x)—&(x)>()᪀⌼ᦪgqr,g,(X)=hi-᜛প$XXXg'(x)<0;—l0..-.g(-e)>g(-l),.-.^^>^=^,ᓄt<(-e)2(-1)-/(-e)-e2/(-D>0.ᦑ⌱A.10.f'(x)᜻ᦪ/(x)(x/0)Ḅ!ᦪ/(-1)=0,#x<0$,xf\x)-3/(x)>0,ᑣug(-l).x>0$/(X)<0J0IJg(x)0,g#(x)="(k)3"ஹ>0,.•.ᦪg(x)x

16ᙠ(7,0)ᓫ⌴,•X<0$g(x)>g(-l),.,.-l0$gU)

17