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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.

The graph of f is given. State the numbers at which f is not differentiable. (Enter your answers as a comma-separated list.)

Learn how to determine where a function is not differentiable based on its graph. This problem involves key calculus concepts like discontinuities, sharp corners, and non-differentiable points. Suitable for advanced high school and college students.

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