Suppose a certain real-valued function f is continuous on the interval [23, 36] and differentiable on (23, 36). Moreover, suppose we also know x} 5 76, for all a: e (23, 36), and an) = 7. {a) We wish to find an explicit upper bound for f(36). Complete the following proof: Proof. First. since f is continuous on the interval .. :: -. o - and differentiable on l'Ji::'v. :3: ~ 1136) n30) W = fl")- Ftearranging this and applying our assumptions on f, we conclude that me) = an) + 6 f'(c) 5 7 + 6 x 76 = 463. then, by -. -':.- l.-..-,; . This completes the proof. (b) Using a similar argument, prove that f(23) 2 525 in the essay box betow. Egym There is no need to use correct Maple syntax or use the equation editor in the essay box below. as long as you response is clear enough for a reader. For example, - rs) may be written as 'f(x}', f"' (c) may be written as 'f'{c}', g and 2 may be written as '4:' and '>=', respectively. a + b c + d The intervals [0, l] and (2, 3) may be written as '[0,1]' and '{2.3}', respectively. may be written as '(a+b}r'{c+d)'. f E Q 253:3" a- I 1; B_I u -5 x. xi Words: I] A