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.