Sketch function from derivatives and limits

Consider a twice-differentiable function f: R → R with: • lim_{x→−∞} f(x) = 0 and lim_{x→+∞} f(x) = 5. • f'(x) > 0 on (−∞, −2) and (1, 3); f'(x) < 0 on (−2, 1) and (3, ∞); f'(x) = 0 only at x ∈ {−2, 1, 3}. • f''(x) < 0 on (−∞, −1) and (−1, 2); f''(x) > 0 on (2, ∞); f'' is undefined at x = 2, but f is continuous everywhere. Tasks: (a) Sketch a qualitatively correct graph of f, marking all local extrema and any inflection points. (b) Is it possible for f to have two local maxima and one local minimum consistent with the above? Justify rigorously. (c) Determine where an inflection point must occur, if any, and explain the sign of the slope immediately before and after x = 2.