J (x) = x" – ¤ – Determine the intervals where f is concave upward and concave downward. Place your answers in the appropriate blanks below. (0.1-) (8.0) 19
J (x) = x" – ¤ – Determine the intervals where f is concave upward and concave downward. Place your answers in the appropriate blanks below. (0.1-) (8.0) 19
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 Intervals
**Function's Second Derivative:**
\[ f''(x) = x^2 - x - 6 \]
**Task:**
Determine the intervals where the function \( f \) is concave upward and concave downward. Place your answers in the appropriate blanks below.
---
**Graph/Diagram Explanation:**
The image shows a blank graph with a vertical and horizontal axis marked with the origin and common interval indicators.
---
### Answers:
**\( f(x) \) is concave upward on the interval(s):**
\[ \text{Enter intervals here} \]
**\( f(x) \) is concave downward on the interval(s):**
\[ \text{Enter intervals here} \]
Utilize the second derivative test to determine these intervals. Find where \( f''(x) = 0 \) or is undefined to locate potential inflection points. Determine the sign of \( f''(x) \) around these points to establish concavity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bdec363-0864-48e9-9cb3-5716963e6c1f%2F3aa4a266-93e0-45ac-8c36-c85027a1b6e6%2Fbh0sidb.jpeg&w=3840&q=75)
Transcribed Image Text:### Concavity and Intervals
**Function's Second Derivative:**
\[ f''(x) = x^2 - x - 6 \]
**Task:**
Determine the intervals where the function \( f \) is concave upward and concave downward. Place your answers in the appropriate blanks below.
---
**Graph/Diagram Explanation:**
The image shows a blank graph with a vertical and horizontal axis marked with the origin and common interval indicators.
---
### Answers:
**\( f(x) \) is concave upward on the interval(s):**
\[ \text{Enter intervals here} \]
**\( f(x) \) is concave downward on the interval(s):**
\[ \text{Enter intervals here} \]
Utilize the second derivative test to determine these intervals. Find where \( f''(x) = 0 \) or is undefined to locate potential inflection points. Determine the sign of \( f''(x) \) around these points to establish concavity.
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