5) [20 marks] Darboux's Property for the derivative: a) Assume that f is differentiable on [a, b] and that f'(a) > 0 while f'(b) 0 while f'(b) a > f'(a), then there exists some c E (a, b) such that f'(c) = a. d) Explain why there is no function F such that F'(x) = f(x) where f(x) = 1 ifreQ 0 if r ( R\\