Determine the open intervals on which the graph is concave upward or concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) g(x) = 9x²x3 concave upward (0, -∞) X concave downward (∞,0) X

Trigonometry (MindTap Course List)
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ChapterP: Prerequisites
SectionP.5: Functions
Problem 9ECP
Question
### Analyzing Concavity of the Graph

To determine the open intervals on which the graph of the function is concave upward or concave downward, we are given the function:

\[ g(x) = 9x^2 - x^3 \]

#### Instructions:
- Enter your answers using interval notation.
- If an answer does not exist, enter DNE (Does Not Exist).

#### Problem Statement:
Determine the open intervals on which the graph is concave upward or concave downward.

#### Example Solution with Errors:

1. **Concave Upward:**
   - Provided Interval: \( (0, -\infty) \)
   - Status: Incorrect
   
2. **Concave Downward:**
   - Provided Interval: \( (\infty, 0) \)
   - Status: Incorrect

#### Additional Resources:
For further understanding and help on this topic, you may refer to:
- **Read It**: A reading material that elaborates on concavity and intervals.
- **Watch It**: A video tutorial that visually explains how to determine concavity.

#### Note:
The intervals provided for concavity (0, -∞) and (∞, 0) are incorrect. Ensure to carefully analyze the function and find the correct intervals where the graph exhibits concave upward or concave downward behavior.
Transcribed Image Text:### Analyzing Concavity of the Graph To determine the open intervals on which the graph of the function is concave upward or concave downward, we are given the function: \[ g(x) = 9x^2 - x^3 \] #### Instructions: - Enter your answers using interval notation. - If an answer does not exist, enter DNE (Does Not Exist). #### Problem Statement: Determine the open intervals on which the graph is concave upward or concave downward. #### Example Solution with Errors: 1. **Concave Upward:** - Provided Interval: \( (0, -\infty) \) - Status: Incorrect 2. **Concave Downward:** - Provided Interval: \( (\infty, 0) \) - Status: Incorrect #### Additional Resources: For further understanding and help on this topic, you may refer to: - **Read It**: A reading material that elaborates on concavity and intervals. - **Watch It**: A video tutorial that visually explains how to determine concavity. #### Note: The intervals provided for concavity (0, -∞) and (∞, 0) are incorrect. Ensure to carefully analyze the function and find the correct intervals where the graph exhibits concave upward or concave downward behavior.
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