The graph of f (x) = 1 2 (1 x)(x2 x 2) is illustrated below. (a) Find the X and Y intercepts. (b) Determine the intervals on which f is decreasing and intervals on which it is increasing.

Graph:

2 0 1 2 31 0 1 2 3 1 2 3 4 (c) Find local minima and local maxima of f (x). (d) Determine concavity intervals for f . Determine inflection points on the graph y = f (x). (e) Determine (vertical and horizontal) asymptotes if any?