Consider the curve given by the function f(x) with x # 1. You are given that f'(x) = -8(2x + 1) and f" (x ) = 48(x + 1) (x - 1)4 (x - 1)5 Compile the following information about f(x) and its graph. Show all your work. (a) [1 point] Find the critical number(s) of f and show your work to justify. (b) [3 points] Find the open interval(s) where f is increasing and the open interval(s) where f is decreasing. Show your work to justify. (c) [3 points] Find the x coordinate(s) of all local minima of f, and all local maxima of f . Show your work to justify. (d) [4 points] Find the open intervals where f is concave up and the open intervals where f is concave down. Show your work to justify. (e) [1 point] Find the x coordinates of all inflection point(s), and show your work to justify