Calculus Writing Assignment: Absolute Extreme Values and Extreme Value Theorem Each problem is worth 5 points. Total Points: 50 Answer each of the problems. Make sure to show all your work. 1) Find all relative extrema in the function f (x) = x 3 + 3x 2 - 24x + 12. 2) Find all points of inflection in the function f (x) = x 3 + 3x 2 - 24x + 12. 3) Find all relative extrema in the function g(x) = (x - 7) 1/3 on the interval [0, 10]. 4) Find all absolute extrema in the function g(x) = (x - 7) 1/3 on the interval [0, 10]. 5) Find all points of inflection in the function g(x) = (x - 7) 1/3 on the interval [0, 10]. 6) Find all relative extrema in the function hx() cos 7) Find all absolute extrema in the function hx() cos 2 3 x on the interval [0, 2]. 2 3 x on the interval [0, 2]. 8) Find all relative extrema in the function k(x) = (x 2 4) 2 on the interval [3, 3]. 9) Find all absolute extrema in the function k(x) = (x 2 4) 2 on the interval [3, 3]. x3 on the interval [0, 5] does not have any absolute extreme values. Does this x2 contradict the Extreme Value Theorem? 10) The function mx()