(a) Show that the function f defined as follows for x = (x1, x2) R2 is a convex function. f(x) = max{x1, x2} (b) If fi and f2 defined on the convex set S are convex functions, show that the following function is also a convex function. f(x) = max{f1(x), 2(x)} (c) If fi and f2 defined on the convex set S are quasiconvex functions, show that the following function is also a quasiconvex function. f(x) = max{f(x), 2(x)} f(x)}