List the local maximum and local minimum values of the function

To find the local maximum and local minimum values of a function, you generally follow these steps:

1. **Find the first derivative** of the function \( f'(x) \).
2. **Set the first derivative equal to zero** to find the critical points, i.e., solve \( f'(x) = 0 \).
3. **Determine the nature of each critical point**:
   - Use the **second derivative test** by finding \( f''(x) \):
     - If \( f''(x) > 0 \), the function has a **local minimum** at that point.
     - If \( f''(x) < 0 \), the function has a **local maximum** at that point.
   - Alternatively, you can use the **first derivative test** to check the sign changes of \( f'(x) \) around the critical points.
4. **Plug critical points into the original function** to find the corresponding function values, which are the local maximum and local minimum values.

If you provide the specific function, I can perform these steps and list the local maximum and minimum values for you.

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Here are five related questions you may find useful:
1. What are the global maximum and minimum values of a function?
2. How does the first derivative test work in determining local extrema?
3. What role does concavity play in identifying local maxima and minima?
4. Can a function have more than one local maximum or minimum?
5. How can graphing help in visualizing local extrema?

**Tip**: Always check the endpoints of a domain when looking for extrema on a closed interval.

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

Learn how to find the local maximum and minimum values of a function by identifying critical points, using the first and second derivative tests. This problem covers key calculus concepts and is suitable for students in Grades 11-12.

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