The discriminant ƒxx ƒyy - ƒxy 2 is zero at the origin for each of the following functions, so the Second Derivative Test fails there. Determine whether the function has a maximum, a minimum, or neither at the origin by imagining what the surface z = ƒ(x, y) looks like. Describe your reasoning in each case. a. ƒ(x, y) = x2y2 b. ƒ(x, y) = xy2 c. ƒ(x, y) = x3y3 d. ƒ(x, y) = 1 - x2y2 e. ƒ(x, y) = x3y2 f. ƒ(x, y) =x4y4

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