Concept explainers
To prove: For all values of x and y such that,
Explanation of Solution
Proof:
Consider the functions,
Then, the given function can be written as,
Find absolute minimum and absolute maximum 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
Substitute
Since the largest functional value is the absolute maximum and the smallest functional value is the absolute minimum, the absolute maximum of
Hence, over the interval
Similarly,
Thus, the product of
Therefore, it is proved that for
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