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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.

The graph of y = f(x) is given below. Use the graph to find each value of x where f is not differentiable.

Explore how to identify the points where a function is not differentiable using graphical analysis. Learn about sharp corners, discontinuities, and other key concepts of differentiability.

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