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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.

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Solution Summary

We derive a formula for the Gaussian curvature of a particular type of surface at a particular point.

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For a general surface of the form z = f(x,y) where f is infinitely differentiable, the Gaussian curvature at the point (x0,y0,f(x0,y0)) ...

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