Determining gaussian curvature

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Let f(x,y) be an infinitely differentiable function. Suppose that

a. f(0,0) = 0

b. f_x(0,0) = 0 and f_y(0,0) = 0.

Consider the surface z = f(x,y). Show that K(0,0) = f_xx(0,0) f_yy(0,0) - f_xy(0,0)^2.

Reference no: EM13133551

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