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The graph of the second derivation f''(x...

The graph of the second derivation f''(x) is given in the following figure. State the x - coordinate of the point of inflection of f. Given reasons for your answer.

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x = 1 is the point of inflection as f'' changes sign from '-' to '+' with f''(1) = 0.
So the concavity of the curve changes from downward to upward.
x = 7 is the point of inflection as f'' changes sign from '+' to '-' with f''(7) = 0. So the concavity of curve changes from upward to downward.
At x = 4, f'' = 0, but f'' does not change sign. So x = 4 is not a point of inflection.
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