Consider the function : R - R. (X) = re. [2 marks] [6 marks) [2 marks] (a) Determine the points where f(x) = 0. (b) Determine all local maxima and minima of the function / (©) Determine where / is strictly increasing and strictly decreasing, respectively (d) Determine where S is convex and concave, respectively, and find all points of inflec- tion. (e) Calculate lim+of(x). (f) Sketch the graph of *100 [4 marks] [3 marks) [3 marks)