[11 marks] 3. Consider the function 5 f($) = 6\"\" $ +332 20 (a) Use the Intermediate Value Theorem to show that there is one point a: = a such that f\"(a) : 0. (b) Prove that there is only one point for which f\"(a) = 0 [Hintz look at the third derivative]. Is this an inection point? Explain. (0) Assume that f\"(ac) > 0 for x a. What does the rst derivative test (applied to f' ) say about f'(x)? ((1) Use the result obtained in part (c) to determine the number of critical points of f