Homework Help is Here – Start Your Trial Now!
Math
Calculus
-6 4 6. 8 a) O f(x) is decreasing on the interval (-4, o0). b) O f(x) is decreasing on the intervals (-0o, -4) and (1, 7). c) O f(x) is decreasing on the intervals (-4, 1) and (7, 0). d) O f(x) is decreasing on the interval (-4, 7). e) O f(x) is decreasing on the interval (-0, 7).

-6 4 6. 8 a) O f(x) is decreasing on the interval (-4, o0). b) O f(x) is decreasing on the intervals (-0o, -4) and (1, 7). c) O f(x) is decreasing on the intervals (-4, 1) and (7, 0). d) O f(x) is decreasing on the interval (-4, 7). e) O f(x) is decreasing on the interval (-0, 7).

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question

thank you!

**Identifying Decreasing Intervals of a Function** **Problem Statement:** Given the graph of \( f'(x) \), determine where \( f(x) \) is decreasing. --- **Graph Analysis:** The graph depicts the derivative \( f'(x) \). The curve crosses the x-axis at points approximately at \( x = -4 \) and \( x = 7 \). The function is negative between these intercepts, specifically on the intervals \( (-\infty, -4) \) and \( (1, 7) \). **Answer Choices:** a) \( f(x) \) is decreasing on the interval \((-4, \infty)\). b) \( f(x) \) is decreasing on the intervals \((-∞, -4)\) and \((1, 7)\). [This is the correct option and is highlighted in blue.] c) \( f(x) \) is decreasing on the intervals \((-4, 1)\) and \((7, \infty)\). **Conclusion:** The correct answer is option b), where \( f(x) \) is decreasing on the intervals where \( f'(x) \) is negative: \((-∞, -4)\) and \((1, 7)\).
Transcribed Image Text:**Identifying Decreasing Intervals of a Function** **Problem Statement:** Given the graph of \( f'(x) \), determine where \( f(x) \) is decreasing. --- **Graph Analysis:** The graph depicts the derivative \( f'(x) \). The curve crosses the x-axis at points approximately at \( x = -4 \) and \( x = 7 \). The function is negative between these intercepts, specifically on the intervals \( (-\infty, -4) \) and \( (1, 7) \). **Answer Choices:** a) \( f(x) \) is decreasing on the interval \((-4, \infty)\). b) \( f(x) \) is decreasing on the intervals \((-∞, -4)\) and \((1, 7)\). [This is the correct option and is highlighted in blue.] c) \( f(x) \) is decreasing on the intervals \((-4, 1)\) and \((7, \infty)\). **Conclusion:** The correct answer is option b), where \( f(x) \) is decreasing on the intervals where \( f'(x) \) is negative: \((-∞, -4)\) and \((1, 7)\).
The image presents a graph of a function \( f(x) \) and several options regarding intervals where the function is decreasing. The graph displays one cycle of the function, with specific intervals of increase and decrease visually represented by peaks and troughs. **Options:** a) \( f(x) \) is decreasing on the interval \( (-4, \infty) \). b) \( f(x) \) is decreasing on the intervals \( (-\infty, -4) \) and \( (1, 7) \). c) \( f(x) \) is decreasing on the intervals \( (-4, 1) \) and \( (7, \infty) \). d) \( f(x) \) is decreasing on the interval \( (-4, 7) \). e) \( f(x) \) is decreasing on the interval \( (-\infty, 7) \). Option b is selected as the correct choice, indicating that the function is decreasing on the intervals \( (-\infty, -4) \) and \( (1, 7) \). These intervals correspond to portions of the graph where the function is moving downward as \( x \) increases.
Transcribed Image Text:The image presents a graph of a function \( f(x) \) and several options regarding intervals where the function is decreasing. The graph displays one cycle of the function, with specific intervals of increase and decrease visually represented by peaks and troughs. **Options:** a) \( f(x) \) is decreasing on the interval \( (-4, \infty) \). b) \( f(x) \) is decreasing on the intervals \( (-\infty, -4) \) and \( (1, 7) \). c) \( f(x) \) is decreasing on the intervals \( (-4, 1) \) and \( (7, \infty) \). d) \( f(x) \) is decreasing on the interval \( (-4, 7) \). e) \( f(x) \) is decreasing on the interval \( (-\infty, 7) \). Option b is selected as the correct choice, indicating that the function is decreasing on the intervals \( (-\infty, -4) \) and \( (1, 7) \). These intervals correspond to portions of the graph where the function is moving downward as \( x \) increases.
Expert Solution
Concept

When f'(x)>0, then f(x) is increasing.When f'(x)<0, then f(x) is decreasing.

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS