a) Prove that any global maximum must also be a local maximum. (b) Prove that, if for a given problem more than one global maximum exists, the value of the objective function must be the same at each....

a) Prove that any global maximum must also be a local maximum. (b) Prove that, if for a given problem more than one global maximum exists, the value of the objective function must be the same at each. (c) Show that a linear function is both convex and concave, but neither strictly convex nor strictly concave.