2021 AP Calculus AB FRQ #4

Let f be a continuous function defined on the closed interval −4 to 6. The graph of f(x), consisting of four line segments, is shown above. Let G be the function defined by G(x) = ∫ from 0 to x of f(t) dt.
(a) On what open intervals is the graph of G concave up? Give a reason for your answer.
(b) Let P be the function defined by P(x) = G(x) * f(x). Find P'(3).
(c) Find lim x→ G(x) / x^2 − 2x.
(d) Find the average rate of change of G on the interval [−4, 2]. Does the Mean Value Theorem guarantee a value c, for −4 to 2, for which G'(c) is equal to this average rate of change? Justify your answer.