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
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)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.5: Functions
Problem 9ECP
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8a57943-65a4-4179-bc90-4de17f531e4f%2F84119095-b9e7-4b68-9481-18b1ab478964%2Fswbah89_processed.png&w=3840&q=75)
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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