Problem 7 Let f(x) = x2 sin # for x # 0 and f(0) = 0. You can use [sin x]' = cos x for all r ER. (a) (4 pts) Find f'(x) for any x * 0. (b) (4 pts) Use the definition of the derivative to show that f is differentiable at x = 0 and f' (0) = 0. 2 (c) (4 pts) Show f' is not continuous at x = 0. (d) (4 pts) Show that there are infinitely many points {In} , in r E (0, 1) such that f' (In ) = 0, n = 1, 2