Determine the intervals on which the function is concave up or down and find the value at which the inflection point occurs. y = 9x – 4x4 (Express intervals in interval notation. Use symbols and fractions where needed.) point of inflection at x = interval on which function is concave up: interval on which function is concave down:
Determine the intervals on which the function is concave up or down and find the value at which the inflection point occurs. y = 9x – 4x4 (Express intervals in interval notation. Use symbols and fractions where needed.) point of inflection at x = interval on which function is concave up: interval on which function is concave down:
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Concavity and Inflection Points
#### Determine the intervals on which the function is concave up or down and find the value at which the inflection point occurs.
**Given Function:**
\[ y = 9x^5 - 4x^4 \]
*Express intervals in interval notation. Use symbols and fractions where needed.*
1. **Point of inflection at \( x \) =**
\(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_)
2. **Interval on which the function is concave up:**
\(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_)
3. **Interval on which the function is concave down:**
\(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_)
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ce675ac-583d-450e-8ae1-ad1f22609723%2F2a92380c-6251-45b7-9d69-db37bfc66ce8%2Fsuiab7d.png&w=3840&q=75)
Transcribed Image Text:---
### Concavity and Inflection Points
#### Determine the intervals on which the function is concave up or down and find the value at which the inflection point occurs.
**Given Function:**
\[ y = 9x^5 - 4x^4 \]
*Express intervals in interval notation. Use symbols and fractions where needed.*
1. **Point of inflection at \( x \) =**
\(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_)
2. **Interval on which the function is concave up:**
\(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_)
3. **Interval on which the function is concave down:**
\(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_)
---
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