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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?

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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.

Use the graph of the function f(x) shown below in order to determine all values of x in the interval -6 < x < 5 where the function is not differentiable.

Analyze the graph of function f(x) to determine all x values where the function is not differentiable. This problem involves identifying sharp corners, cusps, vertical tangents, and discontinuities to understand differentiability and continuity. Suitable for Grades 10-12.

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