AP Calculus AB 2015 Question 5 and Answers

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AP Calculus AB 2015 Free Response Question 5

5. The figure above shows the graph of f', the derivative of a twice-differentiable function f, on the interval [-3,4]. The graph of f' has horizontal tangents at x = -1, x = 1, and x = 3. The areas of the regions bounded by the x-axis and the graph of f' on the intervals [-2,1] and [1,4] are 9 and 12, respectively.
(a) Find all x-coordinates at which f has a relative maximum. Give a reason for your answer.
(b) On what open intervals contained in -3 < x < 4 is the graph of f both concave down and decreasing?
Give a reason for your answer.
(c) Find the x-coordinates of all points of inflection for the graph of f. Give a reason for your answer.
(d) Given that f(1) = 3, write an expression for f(x) that involves an integral. Find f(4) and f(-2).

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