Consider the function f(x) and its derivatives: f ′
(x)= (x 2
+1) 2
1−x 2
and f ′′
(x)= (x 2
+1) 3
2x(x 2
−3)
. (a) [2 points] Find the critical numbers of f(x) and show your work to justify. (b) [2 points] Find the open interval(s) where f is decreasing and the open interval(s) where f is increasing. Show your work to justify your answer. (c) [2 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) [2 points] Find the x - coordinates of all inflection point(s) of f, and show your work to justify.