Problem 2 : Let f(r, y) be a real function, twice-differentiable in both er and y, defined on a domain D C IR2. Assume that fry = fyr at all points in D. Prove that the eigenvalues of the Hessian matrix of f are real. Problem 3 : Let h(x, y) be a real function, twice-differentiable in both r and y, defined on a domain D C R2. Assume that h satisfies Laplace's equation in D, that is ah2 ah2 her thyy = + dy2 = 0 at every point (r, y) in D. Prove that if (a, b) E D is a critical point for h, that is V(h) = (0,0) at (a, b), then (a, b) is a saddle point