Chapter 5.3, Problem 31E

In Exercises 29–32 the graph of the second derivative, $f^{″}\left(x\right)$, is given. Determine the x-coordinates of all points of inflection of $f\left(x\right)$, if any. (Assume that $f\left(x\right)$ is defined and continuous everywhere in $\left[-3,3\right]$.) [HINT: Remember that a point of inflection of f corresponds to a point at which $f^{″}$ schanges sign, from positive to negative or vice versa. This could be a point where its graph crosses the x-axis or a point where its graph is broken: positive on one side of the break and negative on the other.]