suppose that f and g are continuous on [a,b] and differentiable on (a,b). Suppose also that f(a)=g(a) and f'(x)<g'(x) for a<x<b. Prove that f(b)<g(b). [hint: Apply the Mean Value Theorem to the function h=f-g.]

I know that h=f-g is continuous on [a,b] and differentiable on (a,b), but i dont know where to go from there. If you could help me it would be greatly appreciated. Thank you!