免費(fèi)高考必備-高中導(dǎo)數(shù)

高考之導(dǎo)數(shù)篇．1.例yxye2xex0)xyx)yx)yln(1x)yx)]xe1，，ye2x2e1(x(ey2xxxex1yxln(1y)(x)x).f1例(xax1若M{x|f(x)0}'f(x){x|f(x)0}數(shù)a())).a由x當(dāng)a>1,1xa;當(dāng)a<1,ax1.x1xax1xax1/a1x1xayy/x12x12aMP,a1.2在P..例=1+433.=1例yx4llx480y（）．4xy30．4xy30．．x4y50x4y30.80l為4xym0，yxxy44而yx4xy30.y4x35例．(x+2+()221111A.x或=xx或xx或xx或=x3333.ykxkxy,0.5又x2y1圓心為2,1.2222k151kk30.k,k3.223k211yx,或y3.31331,1由(,),,22225//(xy1,222xxx2y1y/xyx2./y1x1.kyky//31x132x31(,)(,)22221y3x,y.3例,，C:yx22x,C:yx2aaCC1212..C:yx22x,C:yx2a122yx22xy'2x2x,x2xC111112①y(x22x)x2)(xx)yxxx11111Q2即(x,xa)(xxxx)2()Cya122222②y2xxx2a22lPQl2x2x210x1x,x221x2xa211212111=aPQ.44a)0x122114a，和.CCyx1223:;;;;.例的定義域?yàn)殚_區(qū)間(a,b)在f(x)()fxab(,)(a,b)）f(x)1個(gè)2個(gè)3個(gè)．4個(gè)y.aOx(,0).a1例設(shè)yf(x)x21.f(x)()fx設(shè)設(shè).f(x)ax3bx2cxd(af(x)ax3bx2cxd(af(x)f(x)ax3bx2cxdax3bx2cx，b0d0，f(x)axcx即3由2，f'(x)axc1311c，，f'()ac0f()a124282a4，c3..f(x)4x33x例y2x4x3由2x40[2,).x2x303112x32x4，y'2x42x322x4x32x8又2x32x4，2x32x4當(dāng)y'0，x2在(2,)，f(2)1y2x4x3y2x4x3的值域是[).3,例xRfx4x33x2coscos16．0cos0fxf(x)aa2fxa.()4()在(,).cos0fxxfxcos.f'(x)x26xf'(x)0x10,x22.cos0x'()fx()fxx0(0,)(222+0-0+f(x)↗↘↗coscoscos13在f(f(x)))cos(xf222416.cos1330cos.f()0cos(cos)0224423110cos.或26226cos0xfx()'()fxx0)(222f'(x)f(x)+0-0+3f(xx0f(0)f(0)cos.16若f(0)0cos0cos0.fx()在(,)(,)(623.f(x),)26cos(,)與(f(x),)24f(x(2aa)a2a1a2a1a0或12a1cosa231110cos(,)(,)a21cos6232622432a1.a4843a0或a1.8a43.([8例a.'()ax1(a1),()()fxfxx11a0在(1,)f'x()()fxa0(x)0,1f'.xa(x)、隨xf'()fx11xa+f'(x)(x)f1當(dāng)1(x)0,在f(x)(1,).x(1,)f'aa11.當(dāng)(x)0,在f'()fxx(,)(,)aa1a0在(1,).()fx11當(dāng)a0在在f(x)(,).f(x)(1,)aa例xf(x)3205(1,0)，yfx'()x0.a,b,c,上上f'x0f'x0上2,,f'x0故在(1,2)f(x)（-，1），（2，+）fx在11xx05由f(x)c,'2（（，'''abc0,得12a4bc0,abc5,a2,b9,c12.f(x)m(xx2,'2又f(x)c,'2m3a,b,c2m32m3f(x)xmx2mx,32|32m3由即f(1)，得m6,m2m5,32a2,b9,c12例x3.fxxbexR23xa與abbfxa0，a,0,4fg1gxaex241212..fae,x由fae，33－則fae3x－ee.3x－3x－令fx3或x312當(dāng)<4xx21f，fffff.當(dāng)>4xx21f，fffff.6ffff，而feff，31fe325又g(x)(a)ex24a＋＋），24]24422a112a＋－＋a44a＋＋）且a6<3.2423故a，.2例=3x在1.=.11f..）ff=f，即ab3ab3=，f.令f若f，故.若f.2.=xyyx.0000∵fxx，00yxx.000xxxx.0000x=.04例4.7xxba；V1.VV21,,(0x2).V(42x)2xx34x24x)1∴.V'4(3x28x12令V0得2'1,x2132而,V'12(x)(x2)132,,'.,V0x132當(dāng)'V0x213212827,.x3131314222.VVV3216221.例yx13yxx8(0x120)..312800080.x1002.54013(.40408)2.517.53128000808x100h(x)x1128000x3100180015h(x)(xx8).x2(0x120),380x1280x4800x8033h'(x)(0x120).640x640x22令當(dāng)當(dāng)?shù)脁80.h'(x)x(0,80)h'(x)0,h(x)80h(x)h(80)11.25.h'(x)h(x).x(80,120)xh(x)在(0,120]..=e()x1=x9()x5xx+或+或+xx+或D.或設(shè)又limf(x)則)xx0D.0fnx)nf()22nnn2n)n)n12nn2在()23、)32、、、、3333（11()2,240000b()3））+，1）2[35()3,22、1、588()32A0CD在()32A））9()543A231D5若x()()fxkfxlimk00002k設(shè)則x0且2aR.=xx=且l與Cxyxl32000.xN.22p+.2xe;2x=.x31x5m3m.Sx++nx－N22222n1*n設(shè)xa.3設(shè)與x.2a和b.beab.baxx4.2xa2x1求當(dāng)a=sinxBxy=9=4故yxx000x5(2x0y′x,即4(x29或0得x0=－=－對(duì)應(yīng)有yyxx00000x(x0000y=1593或34=10(1)0(2)15555(35)3及41l=x或l=－.25xAB(15225A3.=－0≠0時(shí)＜∈(0)(0)fflimx0xx時(shí)當(dāng).10B4.解析：∵f′(1－)－nx(1－)=n(1－)［－)－］,令f′)=0,得2n32-12-1nnxxx=2,易知()在=2時(shí)取得最大值，最大值(2(2)－fxxf22123nn2n2n2n2n2)(2).n2n2nDB6AB8DBCBCxf[(x(k)]f(x)xk)limk0000kf(xk)f(x)1f(xk)f(x)limlim[]00002k2kk0k01f(xk)f(x)1limf(x)1.002k20k01+則=！!＞1或logx=(65)log,e2xeaa33x252(3xx2)x＞1(1)a332.＞1(1233.16.,h=+=+R2x2===(2h)h(2h),23411(2)(2Rh3h4)SRh3h42211h(3R2h)2(2Rhh)(6Rh4h)342322(2Rh)h.3令=32(3)2h2′+0－S=3R.23R2l=xxyCy=xxx,y00000000x011∴=xxxxy00000x0又=xxx2xxxx或x=3.y0000000002x0由知x=3,02y33·3－3==－1.y0022284x0l－1x(33428,f'(x)px)p1[2(2p)x]2令,22p，f(.2p)4()p22p2p∴p.2p[f(x)]4()2pxy,00,a2ky|xx0x20∴,a2yy(xx)0x020令0令.2yx0∴1.2S|xy2xex22x21(x2x2x22x3xx22y22yx22x3xxx2x22x3.xx22yy(x2xe.22xx22x3xxe.x22x322xy1xx3x1111y(3x1x11),y3xx)111xyy.33xx)3xx)1xts則－m25t2t=147,0315121又－2)t1,225t212t×7101572259()15當(dāng)S++n=1當(dāng)1x+22222-1n6=1(得xnnxn1nx)2++=x(nxn1nxxn2x)2S++-1n=1((22.xnxnnxnx2n2n12n2x)32若0對(duì).若.若+1－1.3|a|3|a|0－1