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...

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