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.