Hi. I'm taking an Analysis I course and we just started differentiation. I'm not 100% comfortable with it yet and would appreciate some help on a problem in my textbook. Suppose that f:[0,1] to R is continuous on f(0)= 0, differentiable for x in [0,1], and 0 <= f '(x) <= af(x) for a > 0. Prove that f = 0. (Hint: consider the derivative of (e^(-ax))f(x).) Any help you offer would be greatly appreciated.