1. The problem asks to find the $x$-value where the second derivative $f''(x)$ changes sign from negative to positive. 2. This point is called an inflection point, where the concavity of the function changes. 3. From the description, the graph of $f(x)$ has two local minima near $x=-2$ and $x=2$, and a local maximum near $x=0$. 4. The curve looks like a quartic polynomial with a peak at $x=0$. 5. For a quartic with two minima and one maximum, the inflection point typically lies between the maxima and minima. 6. Since the second derivative changes from negative to positive at the inflection point, and the local maximum is at $x=0$, the inflection point is near $x=0$. 7. Thus, the $x$-value where the second derivative changes sign from negative to positive is approximately $$x=0$$. Final answer: $$\boxed{0}$$