The figure above shows the graph of f'(x), the derivative of a twice-differentiable function f, on the interval [-3, 4]. The graph of f'(x) 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'(x) on the intervals [-2, 1] and [1, 4] are 9 and 12, respectively. Find the x-coordinates of all points of inflection for the graph of f(x). Give a reason for your answer.

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Q: 0.5 -0.5 0.5 --0.5-

A: Local maximum of the function.

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