高考数学复习 知识讲解-导数的几何意义-提高

1234yf(x)f(x)f(x)yf(x)y21xxx21yf(x)f(x)f(x)21xxx21yyf(x)f(x)y1k。AB2xxxxxAByAB21Qx,yy)P(x,y)Q(x0，000MQP、PQ，xO(yy)yy。k00(xx)xxPQ00第1页共11页1Px,fxn2f(x)P(x,f(x))PP0nnn0nPP0PPnnP.yx,yy)P(x,y)，0定义：如右图，当点Q(xQ000即x0PQPTPTPMx0PQxOyxf(xx)f(x)limlimf(x)k。0x0x0x0xx0f(x)yP(x,f(x))x00x0f'(x)0x②f'(x)0f(x)00f(x)f'(x)0x第2页共11页CCCCxlClC22lClC11N(x,f(x));00f(x)xf(x)y00f(x)f()(xx)y00(x,f(x))x，y0000(x,f(x))(x,f(x))xy000000xyxy0000xyf(x)(x,f(x))，0011yf'(x)(xx)(x,f(x))1yxy001111xy00()在x,f(x)当xx的00yff(x)或，f(xx)f(x):f(x)yxx0f(x)xf(x)f(x)00f(x)0xxf(x)xf(x)f(x)在x'000第3页共11页：yf(x)yf(xx)f(x)。yf(xx)f(x)。xxyy/＝。xx0f(xx)f(x)xf(x)f(xx)xf(xx)f(x)xy'limy'lim；y'limx0x0x0f(x)f(x)y'f'(x)lim。0xx0x00x0例1】x1例y.2x1在x1y.2x1y(x1)2xky|2由yP得P，22x1y22(x1)y2x.xP(x，f(x))xyx在000yf(x)(xx)P(x，f(x))y此果在00000x.0第4页共11页x211y）424Ax21，11yx,'y4222x11P)2x5yP2x1x5y，2x11x，y(xx)x2xxx222xxx(xx)xy1yx112xxylim(2xx)2x，，x(xx)x(xx)xx2x0x0yPk，x244y8015x。f(x)3春yM(1,f1yx2f(1)f(1)）'252152M(1,f(1))f(1)，221f'(1)，2f(1)3即f(1)。'例x及P.l和P第5页共11页l和P．(xx)3(xx)3x3x33limx2(xxxx0Pk，1x，xx，3000lkx3x，2200l(xxxx)302000l，(xxxx，302000∴xxxx，3020001x或x.00293x，240991＋.444.例2】xP(1,1).】y3P(1,1)P(1,1).y3xk3y13(x1)y3x2；P(1,1)yx得则321x3P(1,1)(x,x)ky'3x3x32201x000001234331yx.ky1(xx0444第6页共11页1y。x1131f(ax)f(a)x1,1aaa2x0111y(xa)。①a2aa212将a。11113,3Px1k，00xx20x20033P'或P。33132331或yx3233xy。】l22lll.1212l2ll和x12x)x)21223x1x0l1设lx2b，222bx)bx)2bb22，xbx0lbb22221x39llly.3122第7页共11页16y3x3x由得1yx322952y15)即l与l(,.12623又ll与x，(1215221251S.22312x2f'(x)f'(2)，例f(x)yxx2x2yxx2x2(xx2)(x2)1。xxx(xx2x2)xx2x2111f0f'(x)。2x222241(0,)y在x11xxxxxxy，xxxyxxx(xxx)(xxx)xxxxxxxxx(xxx)x1xxxx(xxx)xxx(xxx)111232ylimxxxx(xxx)x2xx04y在x2第8页共11页]444(x)4x2y11∵∴∴，(x2(x(x2)222yx4。x(x2)2yxx41。(x2)2x0x0444x(2xx)y∵∴，(xx)x2x(xx)222yxx)。xx(xx)22yxx)8y'∴。x3xx(xx)2x0x0y'|1∴f'(2)。x2f(xk)f(x)例4.若f'(x)20。02k0k0f[x(k)]f(x)f'(x)limΔ00k0k0f(xk)f(x)1f[x(k)]f(x)limk00000k2k2k0f[x(k)]f(x)11lim21。002k2k0f(xk)f(x)limf'(x)Δ00k0k0f(xk)f(x)1f(xk)f(x)121limlimk0。00002k2k2k0第9页共11页f在0f)2fx02x2x)fxf(1f(1)1f(1f(1)1f'(1)12xf(12x)f(1)2x2x0x0f(12x)f(1)2x02f4xx0x)a若0limffxxfxlim0000xxx0x0fxxfxfxxfx)a00000xxx0x020010000x2xx