https://file.aiquickdraw.com/mathbot/file/1726575683186fz3thipl.jpg

The graph provided shows points \( A(-2, -5) \), \( B(1, -1) \), and \( C(4, 3) \), with the curve passing through these points.

The question asks for the intervals where the graph is concave down. A graph is concave down where its curvature bends downward, meaning the second derivative is negative in that region.

### Analyzing the graph:
1. From \( A \) to \( B \), the graph is concave up (shaped like a cup).
2. From \( B \) to \( C \), the graph is concave down (shaped like a hill).

Thus, the graph is concave down after point \( B(1, -1) \) and onward, which corresponds to the interval \((1, \infty)\).

### Correct answer: \((1, \infty)\)

Would you like further details on concavity or second derivative tests?

### Related questions:
1. How do you determine concavity using the second derivative?
2. What is the significance of inflection points in graphs?
3. How do you find intervals of concavity for more complex functions?
4. How do points like \( B(1, -1) \) relate to concavity changes?
5. How do you differentiate concave up and concave down regions?

### Tip:
For any function, regions where the second derivative is negative indicate concave down behavior.

Learn how to find the intervals where a graph is concave down by analyzing the second derivative and curvature. This problem includes an example where the graph is concave down after point B(1, -1). Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation