Question

The figure below shows the graph of f’ , the derivative of the function f, on the closed interval from x = -2 to x = 6. The graph of the derivative has horizontal tangentlines at x = 2 and x = 4.

Answer 1

- The points of inflection of f(x) in a graph of f'(x) is gotten by just finding the points where the graph moves from increasing to decreasing, and also from decreasing to increasing.

- Thus, we have

- The points where the graph changes from increasing to decreasing is at point (2, 0) and the point where the graph moves from decreasing to increasing is (4, -2.5)

- Thus, the inflection points of the graph of f are at (2, 0), and (4, -2.5)