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List the local maximum and local minimum values of the function

To identify the local maximum and minimum values of the function based on the graph, we need to focus on points where the graph changes direction—either from increasing to decreasing (local maximum) or from decreasing to increasing (local minimum).

From the image, the graph changes directions at the following points:

- **Local maximum**: The graph peaks around \( x = -2 \) and \( x = 4 \), where it switches from increasing to decreasing.
- **Local minimum**: The graph dips around \( x = 1 \) and \( x = 6 \), where it switches from decreasing to increasing.

Based on this:

1. **Local maxima** occur at \( ( -2, 3 ) \) and \( ( 4, 3 ) \).
2. **Local minima** occur at \( ( 1, -3 ) \) and \( ( 6, 0 ) \).

Let me know if you'd like more details on how to identify these points, or if you have any questions!

Here are 5 related questions to explore further:
1. How can you determine if a function has a local maximum or minimum from its first derivative?
2. What are the differences between local and global maxima or minima?
3. How can you identify critical points from a function's equation?
4. What role does the second derivative play in determining concavity at critical points?
5. How can local maxima and minima help in sketching the graph of a function?

**Tip**: When analyzing graphs, always check where the slope changes to help identify maxima and minima effectively.

List the local maximum and local minimum values of the function.

Learn how to identify the local maximum and minimum points of a function by analyzing its graph. Understand where the graph changes direction, including local maxima at (-2, 3) and (4, 3), and local minima at (1, -3) and (6, 0). Suitable for Grades 9-12.

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