https://file.aiquickdraw.com/mathbot/file/1726075692125zow0k93h.jpg

To answer this, let's examine the graph.

From the graph, the function appears to have points where it is **not differentiable**. A function is typically not differentiable at:
1. **Corners** or **cusps** (sharp turns).
2. **Discontinuities** (gaps in the graph).
3. **Vertical tangents** (infinite slope).

### Step-by-step analysis:
- **At \( x = 2 \)**: The function has a sharp corner, so it is not differentiable at this point.
- **At \( x = 4 \)**: There is a cusp or sharp point where the function changes its slope abruptly.
- **At \( x = 5 \)**: There is a gap or discontinuity where the function jumps, making it non-differentiable.

### Answer:
The function is not differentiable at \( x = 2, 4, 5 \).

Would you like further details on how to identify non-differentiable points? Here are related questions for further exploration:

1. What is the difference between a corner and a cusp in terms of differentiability?
2. Can a function be continuous but not differentiable at certain points?
3. How can vertical tangents lead to non-differentiability?
4. What is the relationship between differentiability and smoothness of a graph?
5. What conditions are necessary for a function to be differentiable?

**Tip:** Always check for both continuity and the smoothness of the curve to determine differentiability.

List the points in the graph in the interval 0 < x < 6 at which the function is not differentiable.

Determine points where the function is not differentiable on a graph. This problem focuses on the analysis of differentiability, identifying sharp corners, discontinuities, and other non-differentiable points in the interval 0 < x < 6. Suitable for students in Grades 11-12.

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