2. [20 pts] Sketch the graph of a single function f(x) which satisfies all the following conditions. Label all local maxima and minima, intervals of increase and decrease, points of inflection, concavity and asymptotes. Hint: Using the sign charts of f' and f". (a) f(x) is defined for all real numbers. (b) f'(x) = x'(x-2)e-I (c) f"(x) = x(x -1)(4-c)e (d) lim f(x) = 2 (e) lim f(a) =00 J-+-00 (f) f(0) =0