To determine where the function $f(x)$ is not differentiable, we look for points in the graph that exhibit:

1. Sharp corners or cusps: These are points where the graph has a sharp change in direction, making the slope undefined.
2. Discontinuities: If there is a break or jump in the graph, the function is not continuous and thus not differentiable.
3. Vertical tangents: These occur when the slope becomes vertical (infinite), meaning the derivative does not exist at that point.

Analysis of the Graph:

1. At $x = -2$, there is a sharp corner, meaning the function is not differentiable here.
2. At $x = 2$, there is another sharp corner, leading to non-differentiability here as well.

The points where the function is not differentiable are $x = -2$ and $x = 2$, which matches the answer given: $x = -2, 2$.

Would you like more details on how to detect non-differentiable points in graphs?

Related questions:

1. What are the conditions for differentiability of a function at a point?
2. How does a vertical tangent lead to non-differentiability?
3. Can a function be continuous but not differentiable at certain points?
4. What is the relationship between differentiability and continuity?
5. How do discontinuities affect the differentiability of a function?

Tip:

When analyzing a graph for differentiability, always check for sharp turns, breaks, and vertical slopes, as these are key indicators of non-differentiability.