(完整版)高考導數(shù)題型歸納

高考壓軸題：導數(shù)題型及解題方法（自己總結(jié)供參考）一．切線問題在xx1yf(x)0fxxx()002(a,b)yf(x)f(x)(,())()()()xfxxafxfxbxy000000例9xy160）Am)(myf(x)myf(x)x,f(x)x,f(x)0000于x,mm2）0yx3x3yx3x3x3x3xy015x4y0或）y3e2xye10y1aea2x3yf(x)yg(x)、yf(x)yg(x)、x,f(x),()xfx1122x,x(xx)f(x)yy(xx)f(x)yyx,x1，，1221121212212例yx2y2ex2exye0）yx2y(x22xy10y0或）1f(xg(x)2．設(shè)函數(shù)f(x)p(x)2lnx,g(x)x2lxf(x)p或）p13二．單調(diào)性問題1001例f(x)alnxx(ax22f(x)xef(x)1f(x)ex(kexkx1xf(x)xx222f(x)'或f(x)0'f(x)在m,nf(x)a,b2例f(x)xalnx2+在xa）1(k()(2,)fxf(x)x3x2k32k13）31，aR例f(x)xaxx132a2a2,3三．極值、最值問題。1→→→→1x例f(x)ex(kexkx12xx2g(x)f(x)6xf(x)xmxnx2(1,32ya0a10yf(x)(a1,a1)f(x)21a3f(x)6a或1a3f(x)2111例f(x)xp)xpxpp)x1f(x)p432432(x)axxlnx,aR.2fx()f512a）3R()fxax3xg(x)f(x)f(xx[02]x0例設(shè)a326a,）5，當a0f(x)e2，f(x)ax(a2)xlnx2a）四．不等式恒成立（或存在性）問題。f(x,naf(x)an，＞xm,n,xm,n，f(x)g(x)f(x)g(x)。121212。x,n,x,nf(x)g(x)f(x)g(x)，121212x,n,f(x)g(x)f(x)g(x)01111x,n,x,nf(x)g(x)f(x)g(x)對，。121212x,n,x,n，f(x)g(x)f(x)g(x)對121212f(x)f(x)m,n,xm,n，at(x)f(x)。轉(zhuǎn)化證明t(x)對x12xx12在m,n12100xef(x)e例f(x)e(xlnx)aax2）f(x)x(eax時f(x)axx2）0的例ex1x時a21a,）2x1e，x0f(x)af(x)1xax1）21f(x)alnxa0.xax(2x)1對axe）1）yf(x)Df(x)f(x)，Dg(x)D上，g(x)0恒成立，則稱函數(shù)yf(x)在區(qū)間D上為“凸函數(shù)”，已知實數(shù)m是常數(shù)，x3x4m2mf(x)a,b32f(x)62ba）2f(x)xxaf(ax)f(a)x0f(ax)f(a)e，xf(ax)f(a)eg(a)f(a)xexaeaea五．函數(shù)零點問題1R,f(x)x3(1axyf(x)a例設(shè)a31a1f0，f(3)0a,）3yxxx1(x)lnxx1a(x3,例fa）12f(x)xg(x)exex六．不等式證明問題f(x)g(x)f(x)g(x)alnxbyf(x)(1,fx2y30f(x)x1x當x0x1f(x)lnxx1。當1ae1f(x)與xf(x)axe(a0)xf(x)axkbx(x0)g(x)axblnx,、、kg(x)圖2x2y2ln220(x,y),B(x,y),(xx)p(2,g(2))是112212yyg(x)yg(x)xxx12xx010221f(x)xxax0