Concept explainers
(a)
To find: The theorem guarantees the existence of an absolute maximum value and an absolute minimum value for f if f is a continuous function on
(a)
Answer to Problem 2E
The, Extreme value theorem guarantees that the existence of an absolute maximum value and absolute minimum value for f.
Explanation of Solution
Reason:
Extreme value theorem says that, “If f is a continuous function on a closed interval
(b)
To explain: The steps to find the maximum and the minimum values of the continuous function.
(b)
Explanation of Solution
The steps to find the values of maximum and minimum values of the continuous function are as follows.
Step 1:
Find the first derivative
Step 2:
Take
Step 3:
Check whether the critical number(s) obtained in Step 2 are lies in the given interval or not.
Step 4:
Consider the critical numbers that are lies in the given interval.
Step 5:
Substitute the critical number(s) considered in Step 4 in
Step 6:
From the values obtained in Step 5, identify the value where the function attains its maximum, is called an absolute maximum of
Chapter 4 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning