In Exercises, sketch the graph of a single function that has all of the properties listed.

(a) Continuous for all real numbers

(b) f'(x) > 0 on (-∞, -2) and (0, 3)

(c) f'(x) < 0 on (-2, 0) and (3, 0)

(d) f"(x) < 0 on (-∞, 0) and (0,5)

(e) f"(x) > 0 on (5, ∞)

(f) f'(-2) = f'(3) = 0

(g) f'(0) doesn't exist

(h) Differentiable everywhere except at x = 0

(i) An inflection point at (5, 1)