To determine the values of $x$ where the function $f(x)$ is not differentiable, we need to look at the graph for any points where the following occur:

1. Sharp corners or cusps: Points where the graph changes direction abruptly.
2. Vertical tangents: Points where the slope of the tangent is infinite.
3. Discontinuities: Points where the function is not continuous.

Let's analyze the graph you provided.

Analysis:

1. At $x = -4$: There is a cusp or sharp corner.
2. At $x = -1$: There is a discontinuity, where the function jumps from one value to another.
3. At $x = 3$: There is another cusp or sharp corner.

Conclusion:

The function $f(x)$ is not differentiable at $x = -4$, $x = -1$, and $x = 3$.

Would you like further details on how to identify these points or have any other questions?

Here are some related questions:

1. What is the definition of differentiability and how is it related to continuity?
2. How do vertical tangents affect differentiability?
3. Can a function be continuous at a point where it is not differentiable?
4. How does the derivative behave at a sharp corner?
5. What are some other examples of functions that are not differentiable at certain points?

Tip: When analyzing a graph for differentiability, always check for sharp turns, vertical tangents, and discontinuities—they are the most common reasons for non-differentiability.