高中數(shù)學(xué)圓錐曲線和導(dǎo)數(shù)知識(shí)點(diǎn)總結(jié)

.PFPF2aFF方程為橢圓,1212PFPF2aFF無軌跡,1212PFPF2aFFF,F為端點(diǎn)的線段121212de，點(diǎn)PFdPlFl橢圓方程x2y21(ab0)aa2b2a2b2yyA圖形特征B22FM002xx1FOFA2BB1212B11|x|a,|y|b(c,0)2xac對(duì)稱性長(zhǎng)短軸離心率關(guān)于軸、軸、原點(diǎn)對(duì)稱xy長(zhǎng)軸長(zhǎng)|AA|2a,短軸長(zhǎng)|BB|2b長(zhǎng)軸長(zhǎng)|AA|2a,短軸長(zhǎng)|BB|2b12121212ee焦半徑|MF|aex,|MF|aex||a,||a10201020acos①x2y21x（0ybsin2a2b2.b2ab2xy21,則x2x22y21xyk=000a2ya2b2ab20a2x12k=k0b2ya022Pxy1.,FFPF1F22tanFPFb12122a2b2b22.a.12.2aFF2122aFF2122aFFF,F121212de，PF點(diǎn)PFdPlFl22（ab）a2b2a2b2圖象a,b,cabc222范圍點(diǎn)頂xbayyxabce(1)aF(c,0)F(0,c)焦點(diǎn)22cc＝＝.e2222x2222,0).abyab,0),yxa2b2a2b2xasec或xbtan.ybtansecyab2ax2y21（,FF12a2b2▲▲yyMFexaMFexa10210aMMFexaMFexa12M2020xxF2xy2ba22xyx222101,則xyk=00a2b2ya2b20a2x1k2k=0b2ya0xy2xy2221；a2b2ab22ny0mxny2222▲y1143)2yxp221bxd，PFdPlFl設(shè)p02y2x2pyx▲yxxxxOOOOppFF22px2p22軸x）px2px2py2py21111.x2x222x22為參數(shù)）.t②y2y2y222p21111p＋.2a設(shè)yxyxyM21122002pp2xx＝y(tǒng)yp，x2412121212p，p2，Sθ12k12y20112＝.le當(dāng)01110eeeeecc.aFF1212值FF的1212值e）e）.方xy12xy21(abab2ab2cosxasecxybsintan)參數(shù)為離心角）參數(shù)為離心角）b），R0,,x軸p121222b2）a2b2）ccaapx222ccp2aa一．導(dǎo)數(shù)的定義：f(xx)f(x)1.(1).函數(shù)yf(xxx處的導(dǎo)數(shù)f'(x)y'|lim00x00x0x0f(xx)f(x)(2).函數(shù)yf(x的導(dǎo)數(shù):f'(x)y'limxx0y()()fxxfxyf(xx)f(x)；00xx00yxf'(x)lim0x0二、導(dǎo)數(shù)的運(yùn)算：1mmm①C'0(為常數(shù))(x)'nx；()'(x)'nxn1(x(xx1；nn1nnmnnxnnxx；④xx(e)'ex(a)'alna(a0,且a1)⑥；③⑦⑤xxx(lnx)'1；⑧(logx)'1(a0,a1)xxlnaa[f(x)g(xf'(x)g'(x)[f(x)g(xf'(x)g(x)f(x)g'(x)f'(x)g(x)f(x)g'(x)[f(x)g(x)(g(x)[g(x2yf(g(x))ug(x)()y'g(x)fu)'ug(x)yfu0fxx22xf'f'xfxexsinxf(4（）f(x)，32101316193..C..三．導(dǎo)數(shù)的物理意義333tVSfttt在000ft，即有Vft。000VS(t)aV(t)''四．導(dǎo)數(shù)的幾何意義：fx在xyfxPx,fxkfx。0000yfxxxy。000Px,fxkfx（1yfx00切線0yyfxxx000yfa)fxPx,yPQ(a,b),Q(a,b00yfxQ(a,b)yyfaxx00Q(a,b)fa)例題在曲線y=x+3x+6x-10的切線中，求斜率最小的切線方程；32ky'|26x63(x3當(dāng)x20Pxx0000五．函數(shù)的單調(diào)性：設(shè)函數(shù)yf(x)在某個(gè)區(qū)間內(nèi)可導(dǎo)，f'(x)0f(x)f'(x)0f(x)f'(x)f(x)f(x)f(x)在該區(qū)間內(nèi)單調(diào)遞增f'(x)0在該區(qū)間內(nèi)單調(diào)遞減f'(x)0()yfxyf(x)①f'(x)0f(x)②f'(x)0f(x)yf(x)yf(x)yf(x)f(x)0f(x)0f(x)在該區(qū)間內(nèi)單調(diào)遞增f'(x)0f(x)在該區(qū)間內(nèi)單調(diào)遞減f'(x)0ffc)0lnxf(x)afbf(4),cf)xb<cc<b<ac<a<bb<a<c六、函數(shù)的極值與其導(dǎo)數(shù)的關(guān)系：f(x)xxf(x)f(x)f(x)f(x)f(x)000x000f(x)xf'(x)0f(x)x00在x0f(x)0f(x)f(x)x30f'(x)；f'(x)0xf'(x)0若若若f'(x)f(x)f'(x)f(0)f'(x)f(x)0x00f(x)f(x)f(x)DxxDf(x)f(x)00yf(x)yf(x)）maxyf(x)00min0[a,b][a,b]上f(x)在閉區(qū)間[a,b]f'(x)；f'(x)0f(x)f'(x)0f(a)fb)、f(x)x12xyf(x)在xf'(x)0f'(x)00000f(x)f(x)f'(x)f(x)（f(x)f'(x)f'(x)減f(x)f(x)f(x)（f(x)xRaaf(x)e.，f(x)Rxx若e∴.xx在Rf(x)在Re在Re）e.xxxx為fe.02例）3233222f32令f(x).32323x13+0-0+↘y84↗↗.x例x0x)x.1xxx(x)ln(xg(x)ln(xxf(x)f，，1xx)2x當(dāng)x0f(x)f(x)f(0)x)0，在1x()(0)x()0()()又gx0xgx，gx在gxg1xxx)x0x0x)x1xx，g(x)ln(xx.f(x)ln(x1xx1x2及例4f(x)2x32c、b在x[03]f(x)cc2()663fxaxbx2，f(x)在1及x2f(1)0f(2)0，．x66ab，2412ab．a(chǎn)3，b4即．f(x)2x9x12xc，32()618126(1)(2)fxx2xxx．令f(x)06(xx0有x1x2,'12f(1)58cf(0)