https://file.aiquickdraw.com/mathbot/file/1726696250313fq5wi24f.jpg

The image shows a graph of a polynomial function and a question that asks to "select all the points which are relative minimums." These are points where the function reaches a local minimum in its behavior, meaning that the function has a decreasing trend before the point and an increasing trend after.

### Step-by-step:
1. **Point A**: This is near the top of the graph, likely a local maximum, not a minimum.
2. **Point B**: Appears to be near the peak of a curve, so also a local maximum, not a minimum.
3. **Point C**: Appears to be at a point where the curve is sloping downwards, possibly leading to a minimum further on.
4. **Point D**: This seems to be a point where the curve is sloping upwards, possibly indicating a local minimum.
5. **Point E**: This looks like a low point in the curve, indicating a relative minimum.
6. **Point F**: This point appears lower than the previous, and also seems to indicate another local minimum.
7. **Point G**: Appears to be a local maximum since the curve is rising up to it and then falls afterward.

### Answer:  
- The relative minimums are likely **Point E** and **Point F**, where the function reaches its lowest values locally.

Would you like a detailed explanation of relative minima, or do you have any specific questions about this?

Here are 5 related questions you might want to explore:
1. What is the difference between a global minimum and a local (relative) minimum?
2. How can we use derivatives to find relative minimums of a function?
3. Why is a point of inflection different from a relative minimum?
4. Can there be more than one relative minimum in a polynomial graph?
5. How do relative maximum and minimum points affect the shape of the graph?

**Tip**: When analyzing polynomial graphs, look for turning points where the slope changes from negative to positive for relative minima and from positive to negative for relative maxima.

Select all the points which are relative minimums on the graph of a polynomial function.

Learn how to identify relative minimums on the graph of a polynomial function. This problem involves graph analysis, where you can use derivative concepts to understand turning points. Suitable for Grades 10-12 students looking to deepen their knowledge of calculus and polynomial graphs.

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