The graph shown asks to determine where the function $f(x)$ is not differentiable. A function is not differentiable at points where:

1. There is a sharp corner or cusp.
2. The function has a vertical tangent.
3. There is a discontinuity (either jump or infinite).

By analyzing the graph:

• At $x = -2$, there is a sharp corner, indicating non-differentiability.
• At $x = 0$, there is a sharp turn, again causing the function to be non-differentiable.
• At $x = 2$, there is a jump discontinuity, meaning the function is not continuous at this point, hence not differentiable.

Conclusion:

The function is not differentiable at $x = -2, 0, 2$.

Would you like further details or explanations?

Here are 5 related questions to expand on this topic:

1. What does it mean for a function to be continuous but not differentiable at a point?
2. Can a function have points of non-differentiability without discontinuities?
3. How can we algebraically check for differentiability at a given point?
4. What is the difference between a cusp and a sharp corner in terms of differentiability?
5. What are some real-world examples where non-differentiable functions appear?

Tip: Always check for continuity first when determining differentiability, as differentiability implies continuity.