5.

5 (a) Find a function f which is dened on [0, l] but which is continuous only on (0,1) and differentiable on (01 1) so that the conclusion of the mean value theorem does not hold. That is, so that there is no t: E (0, 1) with f'(c) = m) ma). (1)) Let f be a function dened on the open interval (1, l) which is thrim differentiable at 0. Suppose f"(()) = 0, f\"(0) = 0, and f\"'{0) = 1 show that f has neither a local minimum nor a local maximum at J: = U