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To determine the x-values where the function \( f \) is not differentiable, we need to look for points on the graph where there are:

1. **Sharp Corners or Cusps:** The function has a sudden change in direction.
2. **Vertical Tangents:** The slope becomes infinitely steep.
3. **Discontinuities:** The function jumps or has a break.

Analyzing the provided graph, we can identify these characteristics:

1. At \( x = -4 \): There is a sharp corner or cusp.
2. At \( x = -1 \): There is a discontinuity (the function jumps).
3. At \( x = 1 \): There is a cusp where the graph changes direction sharply.
4. At \( x = 2 \): There is a discontinuity (the function jumps).

Hence, the x-values where \( f \) is not differentiable are:
\[ x = -4, -1, 1, 2 \]

Would you like a more detailed explanation of these points? 

Here are five related questions for further exploration:

1. What is the definition of differentiability at a point?
2. How can you determine differentiability from the derivative of the function?
3. Why is a function not differentiable at a corner or cusp?
4. What are the implications of a function not being differentiable at a point?
5. How does continuity relate to differentiability?

**Tip:** When analyzing a graph for differentiability, always look for sharp changes, breaks, or vertical segments, as these indicate where the derivative does not exist.

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

Analyze a function's graph to find points where the function is not differentiable. Key concepts include sharp corners, cusps, vertical tangents, and discontinuities. Suitable for high school students in Grades 10-12.

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