https://file.aiquickdraw.com/mathbot/file/1726442733962z50g6zkd.jpg

The problem asks about the slopes at labeled points on a graph. Specifically, it asks where the slope is positive or negative and where the greatest and least slopes occur.

### Let's break it down:
1. **Positive slope** occurs when the graph is rising as you move from left to right.
2. **Negative slope** occurs when the graph is falling as you move from left to right.
3. The **greatest slope** refers to the point where the graph is rising the fastest, and the **least slope** refers to the point where the graph is falling the fastest.

### Based on the image:
- At **Point A**, the graph is rising, so the slope is **positive**.
- At **Point B**, the graph is falling, so the slope is **negative**.
- At **Point C**, the graph is falling more sharply, so the slope is **negative** and larger in magnitude.
- At **Point D**, the graph is again rising, so the slope is **positive**.
- At **Point E**, the graph is at its peak, meaning the slope is **zero** or neutral.
- At **Point F**, the graph is falling sharply, so the slope is **negative** and large.

### Answer:
- **Positive slopes** at **A** and **D**.
- **Negative slopes** at **B**, **C**, and **F**.
- **Greatest slope** (most positive) at **D**.
- **Least slope** (most negative and largest magnitude) at **C** or **F**.

Would you like more details on this explanation or the next steps?

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### Related questions:
1. How can we calculate slope more precisely?
2. What are the physical interpretations of slope in real-world scenarios?
3. How does slope relate to velocity in calculus?
4. What is the significance of points where the slope is zero (like at peaks or valleys)?
5. How can you differentiate between steepness and the sign of the slope?

### Tip:
Always visualize slope by thinking of it as movement: rising means positive, and falling means negative!

For the function shown in the figure below, at what labeled points is the slope of the graph positive? Negative? At which labeled point does the graph have the greatest (i.e., most positive) slope? The least slope (i.e., negative and with the largest magnitude)?

Analyze the slopes at different points on a function graph. Learn how to identify where the slope is positive or negative, and find the points with the greatest and least slopes. This lesson covers essential concepts in calculus and rate of change, suitable for high school students in Grades 9-12.

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