Sketch the graph of a function f (x) with all these properties:

a. f'(x) > 0 for x < 0 and for 0 < x < 2

b. f'(x) < 0 for x > 2

c. f'(0) = f'(2) = 0

d. f"(x) < 0 for x < 0 and for x > 1

e. f"(x) > 0 for 0 < x < 1

f. f(−1) = f(4) = 0; f(0) = 1, f(1) = 2, f(2) = 3