Q8 (12 points) Consider the curve given by the function f(x) with x / 3. You are given that f' (x) = - -(2x + 3) 6(x + 3) and (z - 3)4 f"(I) = (x - 3)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 a coordinates of all inflection point(s), and show your work to justify