3. Let {f1, f2, . .., fn} be a finite set of functions from a convex set D to R. (a) Show that if each fi is convex, then the function f defined by f (ac) = max fi(a) iE{1,...,n} is convex. (b) Show that if each fi is concave, then the function f defined by f (a) = min fi(ac ) iE{1,...,n} is concave