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Show 65 Then Y(u,v) So = A(YU du + Yo (Yu du dv) Yv + dv) + Yv + A(YUU du2 + 2 Yuv du dv dv2) Yvv + = that du Yu Yuu 2 + into this Substituting du2 + Yv dv Yuv du dv the + Yvv dv2 for expansion and Y(u,v) simplifying Y(u,v) dY 1 = .!. = 2 Note that uphill) for the respect the bivariate where in to du2 Yuu A (Yu du be is second the du=O we univariate case. -Yv = u = dv Yvv Yv u o - Yvv we to that that be must Y the must be with negative fll(u) in moving are expression it Note have A dv2 derivative of requiring condition Yvv first analog of the condition the + dv) the of dv (indicating positive quantity The Yv + du dY + dV)2 Yv + Yuv + denominator to. negative case dY This negative. (Yu du - 2" Y(uo,vo) = is be special 0 |
