Question44. The discriminant $f_{x x} f_{y y}-f_{x y}{ }^{2}$ 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 $z=f(x, y)$ looks like. Describe your reasoning in each case. a. $f(x, y)=x^{2} y^{2}$ b. $f(x, y)=1-x^{2} y^{2}$ c. $f(x, y)=x y^{2}$ d. $f(x, y)=x^{3} y^{2}$ e. $f(x, y)=x^{3} y^{3}$ f. $f(x, y)=x^{4} y^{4}$