高二數(shù)學(xué)導(dǎo)數(shù)及其應(yīng)用練習(xí)題2

分2xf(x)2）f(x)4xf(x)42xf(x)82xf(x)x2f(x)xex）0,23．已知對任意實數(shù)，有f(x)f(x)gxg(x，且x0時，x，f(x)0g(x)x0），．f(x)0g(x)0，．f(x)0g(x)0，．f(x)0g(x)0，．f(x)0g(x)0xbxb4f(x)在）312）0b1yx）b1）b0b）lx4y80l）4．4xy30．x4y50．4xy30．x4y30e(2，e)6y）x29e24e2e2e22f(x)f(x)yf(x)和yf(x)）axbxcf'(x)f0，8f(x)）x2ff(x)0f5．23．2．3．2elnx2xmx1(0)q:m≥59p:f(x)在p是q的x2（）．f(x)）ffff）0y//ffff）0//ffff）0）0//ffffO1234x//4xx(xf(x)x12x8[M,mf(x)Mm32xxPyP,331xxax5ya323是.若函數(shù)在)a.3a.4，2x3axbx8c在x1及x2f(x)、bx[03]f(x)c32c2()332、.B的xoyfxxxxx12（,Qxf(xPPAPB4,點Pxf(x)1122線求y2(x4)(B(Q.2x3x3.f(x)y32f(x)x2m0xfx有三個不同的實根，求實數(shù)m.3f(x)(ax4x1aR23aa1Rax3？a2gxxx，xa0．fxxahxfxgx1xeefxx,x（≥gx12a12．f(x)xx;2xf(x)8x222f(x)221xex1exex2xe.xxx1．f(x)f(x)，x選(A)exee2xxbxb由f(x)3xb3xbf(x)3x22bxb0.x4y80l4xym0為yxx4y4xyx4xy30A346）7）8）9）B設(shè)點A點B，Tff(2)ff(2)kyB32ABfk,f(2)k,AQkkkO1234xB1．,e12．32313．,24(2)aa3.a21812x3＜x＜.2h4.53x(m)4V(x)2x2(4.53x)9x26x3(m3)3(0＜2V(x)18x18x2(4.53x)18xx).令02當(dāng)11＜0，3處911m22332m1m3m。31）f(x)6x6axb，21x2及f(1)0f0，．f(x)在x66ab，即2412ab．3b4，．a(chǎn)2x9x12xcf(x)，32f(x)6x18x126(x1)(x2)．2x(0x(1f(x)0f(x)0當(dāng)；；當(dāng)(2，3)f(x)0．當(dāng)x1f(x)f(1)5cfcf9c，．x3f(x)f9c．x3f(x)cx2cc2，9c1c9或，c((9)．:令f(x)(x33x2)3x230x1x或11f(x)01x1f(x)0x1f(x)0當(dāng),當(dāng)x,,當(dāng),1x1取得極大值,故所以,函數(shù)在x處取得極小值,在xx1,f(f412,點B(B4).1,n1,4nm1n4n4設(shè)p(,n)，Q(x,y)，yn22xm11ynk，，y2(x4)4又2xm222PQ8y29,n得x.22n2Pm20232Q3b2a01b2，a04得由222）f(x)6x6x,f(2)12,f(2)7,2分2f(x)x2在y7x，即12xy04y分2x3xm3,g(x)6x6x6x(x1)g(x)322令g(x)x0或6分則x,g(xg(x))x00g(x)當(dāng)xg(x)mx1,g(x)m2.分g(0)0由g(x),g(1)0m即30,3m2m20g(x).f(x)AAym(3,分()()fx;21ax2,2,1）或fx;x,2,x2,,2()f)遞增、當(dāng)a或0fx遞增、當(dāng)ax,2,,2,x,2,xa2)f;當(dāng)a2f)或x2,,()fx;當(dāng),,axx,,x,,aa遞增;3a322()fxfxf()312a,2,axmin4aa22()()3afxf32310aaamina33aa46a2，hx2xxxa12∴hx2．x2x10103a20∵x∵ahxh．3a．1hx3ax3∴a．a(chǎn)2，hx2xxxa1∴hx22．x2xa12令hx0202x2xa0．2xx21a0∵，2118a2118a2∴hx0xx，4412當(dāng)xhx，hxx,xx22—0＋hx118a21a3，2403．∵aaefx≥gx成立等價于對任意的（2）解：對任意的x,x都有1212gxx,xefx≥．12當(dāng)x，egx110．xgxxxe在gxgee1∴．maxxaxaxe，a0．a(chǎn)2∵fx1xx22xaxaa1x且e，fx0，0x2fxa2x，exfxf11a∴.2ae1a由12≥≥e，又0a1a≤a≤exaxa≤x＜afx0，x2xaxa若a＜x≤efx0．x2aea2x