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The question is asking to determine all values of \( x \) where the function \( f \) has a horizontal tangent line on the interval \( -9 < x < 9 \), based on the given graph.

### Horizontal Tangents:
A horizontal tangent occurs where the derivative of the function \( f'(x) = 0 \), meaning the slope of the function is zero. These points correspond to local maxima, minima, or points where the graph flattens out (inflection points) without sloping upward or downward.

### Steps to solve:
1. Look for points where the graph of \( f(x) \) is flat, i.e., where the tangent line appears horizontal.
2. Identify those points' corresponding \( x \)-values.

### Observations from the graph:
- There are flat (horizontal tangent) points where the graph changes direction (local maxima or minima). 
- These occur at the following approximate values:
  - \( x \approx -6 \) (local minimum)
  - \( x \approx -2 \) (local maximum)
  - \( x \approx 3 \) (local minimum)
  - \( x \approx 7 \) (local maximum)

Thus, the values of \( x \) where \( f \) has a horizontal tangent line are approximately:
\[
x = -6, -2, 3, 7
\]

You can enter these values into the answer box.

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Do you need more details, or have any questions? Here are five related questions for further learning:

1. What is the formal definition of a critical point?
2. How is the derivative of a function related to finding horizontal tangent lines?
3. What is the difference between a local maximum and a global maximum?
4. How do you compute the exact coordinates of local extrema using calculus?
5. What are inflection points, and how do they differ from points with horizontal tangents?

**Tip:** Horizontal tangents occur where the slope of the function equals zero, which typically happens at local extrema.

Determine all values of x where the function f has a horizontal tangent line on the interval -9 < x < 9.

In this problem, we explore how to determine the values of x where a function has a horizontal tangent line on the interval -9 < x < 9. The key concepts involve calculus, derivatives, and finding critical points where the slope equals zero. This is suitable for high school calculus students.

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