The derivative of a function f is defined by f ′(x) = { 1 − 2 ln (2 − x 2 ) , −5 ≤ x ≤ 2 g(x), 2 < x ≤ 5 , where the graph of g is a line segment. The graph of the continuous function f ′ is shown in the figure above. Let f(3) = 4. a) Find the x-coordinate of each critical point of f and classify each as the location of a relative minimum, a relative maximum, or neither a minimum nor a maximum. Justify your answer. b) Determine the absolute maximum value of f on the closed interval –5 ≤ x ≤ 5. Justify your answer. c) Find the x-coordinates of all points of inflection of the graph of f. Justify your answer. d) Determine the average rate of change of f ′ over the interval –3 ≤ x ≤ 3. Does the mean value theorem guarantee a value of c for –3 < c < 3 such that f ′′ is equal to this average rate of change? Justify your answer.