In: Advanced Math
Each of the following functions has a critical point at the origin. Show that the second derivative test fails there. Determine whether the functions has a local maximum, local minimum, or saddle point at the origin by visualizing what the surface z=f(x, y) looks like. Describe your reasoning.
(a)f(x, y) =x^2y^2
(b)f(x, y) = 1−xy^2