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Each of the following functions has a critical point at the origin. Show that the second...

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Advance Math

Each of the following functions has a critical point at theorigin. Show that the second derivative test fails there. Determinewhether the functions has a local maximum, local minimum, or saddlepoint at the origin by visualizing what the surface z=f(x, y) lookslike. Describe your reasoning.

(a)f(x, y) =x^2y^2

(b)f(x, y) = 1?xy^2

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