Concept explainers
To find: The
Answer to Problem 4RE
The
The absolute
The absolute minimum is
Explanation of Solution
Given:
The function is,
Calculation:
Obtain the first derivative of the given function.
Set
Thus, the value of
Thus, the critical number is
Apply the extreme values of the given interval and the critical number
Substitute
Substitute
Substitute
Since the largest functional value is the absolute maximum and the smallest functional value is the absolute minimum, the absolute maximum of
Therefore, the absolute maxima of
To find the local maximum and minimum find the second derivative.
On further simplification, the second derivative of the function becomes,
Substitute the critical numbers in the second derivative and find the local maximum and minimum as follows.
Substitute
On further simplification, the value of
Thus, the local minimum occurs at
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