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.