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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.

Use the given graph of the function to find the x-values for which f is not differentiable.

Learn how to determine the x-values where a function is not differentiable by analyzing sharp corners, discontinuities, and vertical tangents in the graph. This problem involves key concepts in calculus, including differentiability and continuity, suitable for Grades 11-12.

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