Can someone tell me if my logic in answering the following questions is ok: 1. Suppose that f(x) and g(x) are convex on (a,b). Show that the functions h(x)=max[f(x), g(x)] is also convex on (a,b). -I said that since f and g are convex their second derivatives are not equal to zero in (a,b) and then said since h is the max of f or g, that h also has a second derivative in (a,b) not equal to zero implying it is also convex. 2. Let f be differentiable on (a,b). Show that if f is convex if and only if for all x, y in (a,b): f(y)-f(x)>(y-x)f'(x) -I'm at a loss on this one.