Final answer:
To find the x-coordinates of the inflection points, we need to locate the values of x for which the second derivative changes sign from positive to negative or from negative to positive. In the given graph, the second derivative is positive to the left of x = 0 and negative to the right of x = 0. Therefore, the inflection point occurs at x = 0.
Step-by-step explanation:
An inflection point of a function f occurs where the second derivative f'' changes sign. In other words, it is a point where the concavity of the function changes. To find the x-coordinates of the inflection points, we need to locate the values of x for which the second derivative changes sign from positive to negative or from negative to positive. In the given graph, the second derivative is positive to the left of x = 0 and negative to the right of x = 0. Therefore, the inflection point occurs at x = 0. So, the x-coordinate of the inflection point of f is 0.