Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(c)=0. If Rolle's Theorem cannot be applied, explain why not.
Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(c)=0. If Rolle's Theorem cannot be applied, explain why not.
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
Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(c)=0. If Rolle's Theorem cannot be applied, explain why not.
![**Problem 21**
Given the function \( f(x) = \cos(\pi x) \).
The domain for this function is specified as the interval \([0, 2]\).
### Explanation
The function describes a cosine wave that fluctuates as \( \pi \) multiplies the variable \( x \). The domain \([0, 2]\) indicates that the values of \( x \) range from 0 to 2, inclusive.
This means that for any calculations or graphing involving this function, you are only considering \( x \)-values within this interval. The cosine function with an argument of \( \pi x \) will complete one full wave cycle over this defined domain, starting at a cosine value of 1 (when \( x = 0 \)) and ending again at 1 (when \( x = 2 \)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3651bc5-cd2c-43d5-bdfb-11943a13f854%2F94c5f9ec-2603-48e7-bb78-aef78c63bdd4%2Fi5s178_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 21**
Given the function \( f(x) = \cos(\pi x) \).
The domain for this function is specified as the interval \([0, 2]\).
### Explanation
The function describes a cosine wave that fluctuates as \( \pi \) multiplies the variable \( x \). The domain \([0, 2]\) indicates that the values of \( x \) range from 0 to 2, inclusive.
This means that for any calculations or graphing involving this function, you are only considering \( x \)-values within this interval. The cosine function with an argument of \( \pi x \) will complete one full wave cycle over this defined domain, starting at a cosine value of 1 (when \( x = 0 \)) and ending again at 1 (when \( x = 2 \)).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
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