Suppose a certain real-valued function f is continuous on the interval [33, 50] and differentiable on (33,50). Moreover, suppose we also know f'(x) ≤ 96, for all x € (33,50), and f(47) = 14. (a) We wish to find an explicit upper bound for f(50). Complete the following proof: Proof. First, since f is continuous on the interval Click for List and differentiable on Click for List then, by Click for List Click for List f(50)-f(47) = f'(c). = 50-47 Rearranging this and applying our assumptions on f, we conclude that f(50) = f(47) +3f' (c) ≤ 14+3 × 96 = 302. This completes the proof. (b) Using a similar argument, prove that f(33) > -1330 in the essay box below.