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To find the x-values where the graph of \( f(x) \) has a horizontal tangent, we need to identify the points where the slope of the tangent line is zero. These points occur at local maxima and minima of the function.

From the graph you provided, we can observe the following points where the slope of the tangent appears to be horizontal:

1. **Local Maximum:** Around \( x = -3 \).
2. **Local Minimum:** Around \( x = 3 \).

Therefore, the x-values where \( f(x) \) has a horizontal tangent are approximately \( x = -3 \) and \( x = 3 \).

Would you like more details on how these points were determined or have other questions on this topic?

Here are some related questions you might find interesting:
1. How can you determine the exact x-values if given the equation of the function?
2. What is the significance of finding points where the tangent is horizontal in real-world applications?
3. How would the method change if we were looking for points where the tangent is vertical?
4. Can you explain how to find the second derivative and its role in confirming maxima and minima?
5. What are the possible mistakes one might make in visually estimating these points from a graph?

**Tip:** When examining a graph to find horizontal tangents, always look for changes in the direction of the curve which typically occur at peaks and valleys.

Estimate and list the value of x where f(x) has a horizontal tangent.

Learn how to estimate the x-values where the function f(x) has a horizontal tangent based on its graph. This problem involves key calculus concepts such as finding the derivative and identifying critical points.

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