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The image shows a graph with labeled points \( A \), \( B \), \( C \), \( D \), \( E \), and \( F \), as well as a table that asks you to match the slopes with the respective points.

Here's how to approach this:

1. **Interpret the slopes:**
   - Negative slopes indicate the curve is decreasing at the given point.
   - A slope of \(0\) means the tangent line is horizontal, suggesting the point is a local maximum or minimum.
   - Positive slopes indicate the curve is increasing at the given point.

2. **Examine the points:**
   - Point \( A \) is at a local maximum (slope \( = 0 \)).
   - Point \( B \) is on a downward slope (slope \( < 0 \)).
   - Point \( C \) is at a local minimum (slope \( = 0 \)).
   - Point \( D \) is on an upward slope (slope \( > 0 \)).
   - Point \( E \) is on a steep upward slope (slope \( > 0 \)).
   - Point \( F \) is on a downward slope (slope \( < 0 \)).

3. **Match points with slopes:**
   - \( A \): Slope is \( 0 \).
   - \( B \): Slope is negative, likely close to \( -1 \) based on the curve.
   - \( C \): Slope is \( 0 \) (local minimum).
   - \( D \): Slope is positive, likely \( 1 \) or \( 2 \).
   - \( E \): Slope is steep and positive, likely \( 2 \).
   - \( F \): Slope is negative, steeper than at \( B \), likely \( -3 \).

Thus, the probable matching is:
- Slope \( -3 \) → Point \( F \)
- Slope \( -1 \) → Point \( B \)
- Slope \( 0 \) → Point \( A \) or \( C \)
- Slope \( 1 \) → Point \( D \)
- Slope \( 2 \) → Point \( E \)

Would you like further clarification on these matching steps or a detailed explanation of any specific part?

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Here are some related questions you might find useful:
1. How do you determine the slope of a curve at a point?
2. What is the significance of local maxima and minima in a function?
3. How can you estimate slope values visually from a graph?
4. What is the relationship between the derivative and the slope of a curve?
5. How does the steepness of a curve relate to the magnitude of the slope?

**Tip:** In calculus, the slope of a curve at a point is given by the derivative of the function at that point. Understanding the derivative can help you analyze the behavior of the curve.

Match the points labeled on the curve in the figure with the given slopes. Points labeled are A, B, C, D, E, and F. The slopes to match are: -3, -1, 0, 1, 2.

Learn how to match points on a curve with specific slopes using calculus concepts such as derivatives. This problem focuses on identifying slope values at labeled points A, B, C, D, E, and F, and matching them with the given slopes -3, -1, 0, 1, 2. Suitable for students in Grades 11-12.

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