The graph of the derivative, f '(x), is given. Determine the x-coordinates of all points of inflection of f(x), if any. (Assume that f(x) is defined and continuous everywhere in [-3, 3]. If there are more answer blanks than inflection points, enter NONE in any remaining spaces)

Question

(x1) = Incorrect: Your answer is incorrect. (smaller value)
(x2) = Correct: Your answer is correct. (larger value)

Answer 1

Look at the graph. f(x) has points of inflection where f''(x) = 0.

But f''(x)=0 means that f'(x) has a min or max. So, observe the x-values where the given graph has a minimum or maximum. That is where f(x) has a point of inflection.