Concept explainers
Show that
To prove: For all values of x,
Explanation of Solution
Proof:
Find absolute minimum and absolute maximum of the function
Observe that
Therefore,
So, find the critical points of the function
Differentiate
Set
Thus, the critical points are
Apply the extreme values of the given interval and the critical number in
Substitute
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
Thus, over the interval
Can be expressed as,
Therefore, for all values of x,
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