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In this question, the graph of the function \( f(x) \) is displayed, and we are asked to determine how many values of \( x \) in the interval \((-2, 5)\) make \( f(x) \) **not differentiable**.

To determine where \( f(x) \) is not differentiable, we look for points where one of the following occurs:

1. **Discontinuity**: The graph jumps or has a break.
2. **Sharp Corner or Cusp**: The slope changes abruptly, so the derivative doesn't exist.
3. **Vertical Tangent**: The derivative becomes infinite.

### Examining the graph:
1. **At \( x = -1 \)**: There is a sharp corner or cusp, which makes the function not differentiable at this point.
2. **At \( x = 2 \)**: There is a vertical dashed line indicating a discontinuity, meaning the function is not differentiable here.
3. **At \( x = 4 \)**: There is another sharp corner (where the graph sharply changes direction), so the function is not differentiable at this point either.

Thus, the function is **not differentiable** at three values: \( x = -1 \), \( x = 2 \), and \( x = 4 \).

### Answer:
- The correct choice is **3** values where \( f(x) \) is not differentiable.

Would you like more details, or do you have any other questions?

Here are five related questions to deepen your understanding:
1. What is the difference between continuity and differentiability?
2. How can you identify a discontinuity on a graph?
3. Can a function be continuous but not differentiable at a point? Why?
4. What is the geometric interpretation of a vertical tangent?
5. How do cusps or sharp corners affect the differentiability of a function?

**Tip:** Always check for points of discontinuity, cusps, and vertical tangents when determining where a function is not differentiable!

For how many values of x is f(x) not differentiable on the interval (-2, 5)?

Identify the points where the function f(x) is not differentiable on the interval (-2, 5) by analyzing discontinuities, sharp corners, and vertical tangents. This problem helps students understand the key differences between continuity and differentiability.

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