5. Unconstrained Optimization (a) Use the definition of convexity to prove that the sum of two convex functions is convex. (b) Use the Hessian to prove that the sum of two convex functions is convex. You may assume that the functions are twice continuously differentiable. (c) Consider the function f(x) = axAx + brac + c, where A is a symmetric d x d matrix. Derive the Hessian of f. Under what conditions on A is f convex? Strictly convex