Use the graph to identify absolute maximum and absolute minimum values for the function on the interval [-3,3]. 3 f(x) = 4x 1 + x² 2- 1+ + 0 -3 -2 -1 2 3 x -2 3 1
Use the graph to identify absolute maximum and absolute minimum values for the function on the interval [-3,3]. 3 f(x) = 4x 1 + x² 2- 1+ + 0 -3 -2 -1 2 3 x -2 3 1
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...
Related questions
Question
100%
![### Determining Absolute Maximum and Minimum Values
**Problem Statement:**
Use the graph to identify the absolute maximum and absolute minimum values for the function on the interval \([-3, 3]\).
#### Function Description:
The function given is:
\[ f(x) = \frac{4x}{1 + x^2} \]
#### Graph Description:
- The graph is plotted with \( x \)-axis ranging from \(-3\) to \( 3 \).
- The \( y \)-axis ranges from \(-3\) to \( 3 \).
- The function appears to be smooth with evident local extrema.
#### Notable Points on the Graph:
- The function starts below the \( x \)-axis around \((x, y) = (-3, -1.2)\).
- It crosses the \( y \)-axis at the origin (0,0).
- The function reaches a local minimum around \((x, y) = (-1, -2)\).
- It then increases and peaks at a local maximum of approximately \( (1, 2) \).
- Finally, it lessens and levels off slightly below \( y = 1 \) as \( x \) approaches 3.
#### Options to Identify:
1. **Option A:**
- There is no absolute maximum, but the absolute minimum, \(-2\), occurs when \( x = -1 \).
2. **Option B:**
- The absolute maximum, \(1\), occurs when \( x = 2 \), and the absolute minimum, \(-1\), occurs when \( x = -2 \).
3. **Option C:**
- The absolute maximum, \(2\), occurs when \( x = 1 \), and the absolute minimum, \(-2\), occurs when \( x = -1 \).
4. **Option D:**
- The absolute maximum, \(2\), occurs when \( x = -1 \), and the absolute minimum, \(-2\), occurs when \( x = 1 \).
#### Correct Analysis:
- By observing the graph, the absolute maximum value of the function \( f(x) \) on the interval \([-3, 3]\) is indeed \(2\), which occurs at \( x = 1 \).
- The absolute minimum value of the function \( f(x) \) on the interval \([-3, 3]\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46a4dff8-7f9e-4127-9d1e-ef0349b76ae2%2F7d78ae6b-fcf6-4fff-9078-af9f2d94669e%2Fmhuwjuo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining Absolute Maximum and Minimum Values
**Problem Statement:**
Use the graph to identify the absolute maximum and absolute minimum values for the function on the interval \([-3, 3]\).
#### Function Description:
The function given is:
\[ f(x) = \frac{4x}{1 + x^2} \]
#### Graph Description:
- The graph is plotted with \( x \)-axis ranging from \(-3\) to \( 3 \).
- The \( y \)-axis ranges from \(-3\) to \( 3 \).
- The function appears to be smooth with evident local extrema.
#### Notable Points on the Graph:
- The function starts below the \( x \)-axis around \((x, y) = (-3, -1.2)\).
- It crosses the \( y \)-axis at the origin (0,0).
- The function reaches a local minimum around \((x, y) = (-1, -2)\).
- It then increases and peaks at a local maximum of approximately \( (1, 2) \).
- Finally, it lessens and levels off slightly below \( y = 1 \) as \( x \) approaches 3.
#### Options to Identify:
1. **Option A:**
- There is no absolute maximum, but the absolute minimum, \(-2\), occurs when \( x = -1 \).
2. **Option B:**
- The absolute maximum, \(1\), occurs when \( x = 2 \), and the absolute minimum, \(-1\), occurs when \( x = -2 \).
3. **Option C:**
- The absolute maximum, \(2\), occurs when \( x = 1 \), and the absolute minimum, \(-2\), occurs when \( x = -1 \).
4. **Option D:**
- The absolute maximum, \(2\), occurs when \( x = -1 \), and the absolute minimum, \(-2\), occurs when \( x = 1 \).
#### Correct Analysis:
- By observing the graph, the absolute maximum value of the function \( f(x) \) on the interval \([-3, 3]\) is indeed \(2\), which occurs at \( x = 1 \).
- The absolute minimum value of the function \( f(x) \) on the interval \([-3, 3]\)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning