https://file.aiquickdraw.com/mathbot/file/1727406084226v6ttidjq.jpg

In this image, you're asked to identify which points are relative minimums based on the graph.

### Analysis of the Graph:
- A relative minimum occurs where the graph changes from decreasing to increasing (a local low point).
- The graph has labeled points: (-6,0), (0,4), (2,0), and (5,0).

From the graph:
- At \( (-6,0) \), the graph is decreasing before this point and increasing after it. Therefore, \( (-6,0) \) is a **relative minimum**.
- At \( (0, 4) \), the graph is increasing both before and after, so this is not a minimum.
- At \( (2, 0) \), the graph is decreasing before this point and increasing after, so \( (2,0) \) is another **relative minimum**.
- At \( (5, 0) \), the graph appears to be flat or undefined after this point, so it does not seem to be a relative minimum.

### Conclusion:
The relative minimum points are:
- \( (-6, 0) \) (Option C)
- \( (2, 0) \) (Option A)

Would you like a detailed explanation on any aspect, or do you have more questions?

Here are 5 follow-up questions for further understanding:
1. What is the difference between a relative minimum and an absolute minimum?
2. Can there be more than one relative minimum on a graph?
3. How do you calculate the relative minimum points analytically for a function?
4. What is the importance of critical points in determining minimums and maximums?
5. How can you confirm whether a point is a minimum or maximum using derivatives?

**Tip:** Relative minimums occur where the slope changes from negative to positive, which corresponds to the sign change of the first derivative of a function.

Which points are relative minimums based on the given graph?

Learn how to identify relative minimum points on a graph. This problem involves graph analysis and calculus concepts, focusing on relative minimums where the graph changes from decreasing to increasing. Suitable for students in Grades 11-12.

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