https://file.aiquickdraw.com/mathbot/file/1730540793196jafrf9tn.jpg

To solve this problem, we need to analyze the slopes at the labeled points on the curve (points A through F) and match each point with its corresponding slope. Let's go through each point:

1. **Point A**: The curve is slightly increasing at point A, so the slope is positive but close to zero. It looks like a very shallow upward slope.

2. **Point B**: The curve has reached a local maximum at B, meaning the slope here is zero.

3. **Point C**: The slope at C is negative as the curve is descending. The slope seems steep here, so it could correspond to a large negative slope.

4. **Point D**: This is a local minimum, meaning the slope is zero at D.

5. **Point E**: The slope at E is positive as the curve is increasing steeply. It looks like a large positive slope.

6. **Point F**: The curve is decreasing slightly, suggesting a small negative slope.

Now, we match each point to the slopes provided:

- **Slope -3**: This is a steep negative slope, which seems to match point C.
- **Slope -1**: A moderately negative slope, which could fit point F.
- **Slope -1/2**: A smaller negative slope, likely for point A if it's slightly decreasing there.
- **Slope 0**: This corresponds to points where the slope is zero, matching points B and D (local extrema).
- **Slope 1**: A positive slope, possibly fitting point A if it is slightly increasing.
- **Slope 2**: A steeper positive slope, which could fit point E.

### Final Matching:
- **Slope -3** ➔ **Point C**
- **Slope -1** ➔ **Point F**
- **Slope -1/2** ➔ **Point A**
- **Slope 0** ➔ **Points B and D** (either order)
- **Slope 1** ➔ **Point A or B** (adjust based

Match the points labeled on the curve below with the given slopes in the following table.

Learn how to match labeled points on a curve with specified slopes by analyzing the tangent lines at each point. This exercise introduces key calculus concepts like identifying positive, negative, and zero slopes at critical points. Suitable for Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation