Consider the function f: R R. f(x) = x²e. (a) Determine the points where f(x) = 0. (b) Determine all local maxima and minima of the function f. (c) Determine where f is strictly increasing and strictly decreasing, respectively. (d) Determine where f is convex and concave, respectively, and find all points of inflec- tion. (e) Calculate lim,400 f(x). (f) Sketch the graph of f. [2 marks] [6 marks] [2 marks] [4 marks] [3 marks] [3 marks]