Given f(x) = 100 (x5 - 5x4 ), f'(x) = 20 x'(x - 4) f"(x) = =x(x-3), answer the following questions. Note that f(0) = 0, f(3) = - ~ -1.62 and f(4) = -54 ~ -2.56. (a) List the critical point(s) (if any) of f (x). (b) Classify each critical point in (a) as a point where either a local maximum, local minimum or neither occurs. (c) State the interval(s) where f(x) is increasing and the interval(s) where f(x) is decreasing. (d) State the interval(s) where f(x) is concave up and the interval(s) where f(x) is concave down. (e) List the inflection point(s) (if any) of f(x). (f) Sketch the graph of f(x)