From the graph of $y = f(x)$, we need to determine where the function is not differentiable. A function is not differentiable at points where there is:

1. A sharp corner or cusp.
2. A vertical tangent.
3. A discontinuity (jump or hole).

Observations:

• From the graph, I can see that the function has sharp turns and breaks at certain points.

1. First $x$-value where $f(x)$ is not differentiable:

• The first sharp corner occurs at $x = -4$, indicating that $f(x)$ is not differentiable there.

2. Next $x$-value where $f(x)$ is not differentiable:

• Moving from left to right, the next discontinuity (a jump) occurs at $x = 1$.

3. Final $x$-value where $f(x)$ is not differentiable:

• Continuing to the right, there's another sharp turn at $x = 3$, where $f(x)$ is also not differentiable.

Answers:

1. $x = -4$
2. $x = 1$
3. $x = 3$

Would you like further details or have any questions? Here are 5 related questions to expand on this concept:

1. What is the formal definition of differentiability?
2. How can you tell if a function is continuous but not differentiable at a point?
3. What types of functions are always differentiable?
4. What are the key differences between continuity and differentiability?
5. Can a function be differentiable but not continuous?

Tip: When checking for differentiability, always look for points where the slope changes abruptly or the graph breaks.