7. (8 marks) Assume that f is continuous and differentiable on (oo,oo). Consider the interval [(1,1)] where a

7. (8 marks) Assume that f is continuous and differentiable on (00, Consider the interval [a, b] where a < b are real numbers. Which of the following statement(s) is/are TRUE? If you believe it is true, justify your reasoning. If you believe it is false, show it with an example. (a) There is a number c in the interval [a, b] such that f(c) is the absolute minimum of f on [a, b]. (b) There is a number c in the interval (a, b) such that f'(c) o. (c) If f(b) < 7 < f(a), then there exists a number c in the interval (a, b) such that f (c) 7 (d) If f (a) 7 and f(b) O, then there exists a number c in the interval (a, b) such that f' (c)