https://file.aiquickdraw.com/mathbot/file/173005964714387ovt81i.jpg

To analyze this graph and determine the local extrema, let's examine the peaks and troughs along the curve. 

The graph shows a function that appears to have:
1. **A local maximum** at approximately \( x = 0 \), where the function reaches its highest point around \( y = 5 \).
2. **No local minimum** in the visible part of the graph, as there is no lowest turning point; the curve continues downward without turning back up.

Thus, the answer is:
- **Local Maximum:** \( (0, 5) \)
- **Local Minimum:** DNE (Does Not Exist)

Would you like more details on finding local extrema, or have any other questions?

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Here are some additional questions related to this topic:

1. How do we determine if a critical point is a local maximum or minimum?
2. What is the difference between local and absolute extrema?
3. How can we find local extrema using calculus instead of just the graph?
4. What types of functions typically have both a local maximum and minimum?
5. How do we interpret intervals of increasing and decreasing in relation to local extrema?

**Tip:** For polynomial functions, local extrema occur where the derivative is zero or undefined, indicating possible peaks or troughs in the curve.

Use the graph to determine the locations and type of the local extrema. Write DNE for all extrema that do not exist. Separate multiple answers with a comma, if necessary.

Explore how to determine the locations and types of local extrema from a graph. This problem involves analyzing a function's graph to find local maximum and minimum points. Suitable for high school students learning calculus or graph analysis.

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