https://file.aiquickdraw.com/mathbot/file/172949554650380zkg9zb.jpg

Based on the graph you provided, let's address each question in turn:

1. **For what values of \( x \) does the function \( f \) have a local (relative) maximum on \( [0, 8] \)?**
   - From the graph, there is a local maximum at \( x = 4 \) where the curve peaks before descending again. 
   - **Answer:** \( x = 4 \)

2. **For what values of \( x \) does the function \( f \) have a local (relative) minimum on \( [0, 8] \)?**
   - The graph shows a local minimum at \( x = 6 \), where the curve dips before rising again.
   - **Answer:** \( x = 6 \)

3. **Find the absolute maximum value for the function \( f \) on the interval \( [0, 8] \).**
   - The highest point on the graph is at \( x = 0 \), where \( f(0) = 5 \).
   - **Answer:** The absolute maximum is \( 5 \).

4. **Find the absolute minimum value for the function \( f \) on the interval \( [0, 8] \).**
   - The lowest point on the graph is at \( x = 6 \), where \( f(6) = 0 \).
   - **Answer:** The absolute minimum is \( 0 \).

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Would you like further details on any of these? Here are five related questions to consider:

1. What is the difference between local and absolute extrema?
2. Can a function have more than one absolute maximum or minimum?
3. How does the derivative of a function relate to its local maxima and minima?
4. Can a function have a local maximum at an endpoint of its interval?
5. What happens if a function has no local extrema on a given interval?

**Tip:** Always check endpoints of the interval when looking for absolute maximum and minimum values!

For what values of x does the function f have a local (relative) maximum on [0, 8]? For what values of x does the function f have a local (relative) minimum on [0, 8]? Find the absolute maximum value for the function f on the interval [0, 8]. Find the absolute minimum value for the function f on the interval [0, 8].

Learn how to determine local maximum and minimum points, as well as the absolute extrema of a function, by analyzing a graph over the interval [0, 8]. The function graph shows local and absolute extrema at specific points, making it a perfect example for pre-calculus or calculus students.

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