For each problem, locate the critical points and evaluate the Hessian matrix at each critical point.

a. \(f(x, y)=(x+y)^{2}\).

b. \(f(x, y)=x^{2} y+x y^{2}\).

c. \(f(x, y)=x^{4} y+x y^{4}-x y\).

d. \(f(x, y, z)=x y+x z+y z\).

e. \(f(x, y, z)=x^{2}+y^{2}+x z+2 z^{2}\).