https://file.aiquickdraw.com/mathbot/file/1727311510970gwyewq8c.jpg

The problem asks for the \( x \)-values where the function \( h(x) \) is not differentiable.

### Key points to consider:
- A function is **not differentiable** at points where there is a discontinuity, a cusp, a sharp corner, or a vertical tangent.
- The graph indicates:
  1. **At \( x = -4 \)**: There's a **vertical tangent**, which means the slope is undefined, so the function is not differentiable here.
  2. **At \( x = 0 \)**: The graph shows a sharp **cusp** or **corner**. The slope from the left and right sides do not match, making the function non-differentiable here.
  3. **At \( x = \frac{3}{2} \)**: There's no visible discontinuity, cusp, or sharp corner at this point. It looks smooth.
  4. **At \( x = 5 \)**: The graph shows a **sharp turn**, making the slope undefined, so the function is also not differentiable here.

### Conclusion:
The function is **not differentiable** at:
- \( x = -4 \) (due to vertical tangent),
- \( x = 0 \) (due to cusp),
- \( x = 5 \) (due to sharp turn).

So, the correct answers are:
- A: \( -4 \)
- B: \( 0 \)
- D: \( 5 \)

Would you like more detailed explanations or clarifications on any part of this? 

Here are five related questions to expand on this:
1. What conditions make a function non-differentiable at a point?
2. How does a vertical tangent affect differentiability?
3. What are the common visual indicators of non-differentiability on a graph?
4. What is the difference between a cusp and a corner in terms of differentiability?
5. Can a continuous function be non-differentiable? Why?

**Tip**: If the slope from the left and right sides at a point differ, it indicates a sharp corner, which implies non-differentiability.

Function h is graphed. The graph has a vertical tangent at x = -4. Select all x-values for which h is not differentiable.

Learn how to determine points of non-differentiability from a graph, focusing on vertical tangents, cusps, and sharp turns. This problem illustrates a vertical tangent at x = -4, a cusp at x = 0, and a sharp turn at x = 5.

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