Concept explainers
a)
To Estimate: The absolute maximum and minimum values (round off up to two decimals) of the function from its graph.
a)
Answer to Problem 57E
The absolute maximum value of
The absolute minimum value of
Explanation of Solution
Given:
The function
Graph:
Use the online graphing calculator to draw the graph of the function
Calculation:
From Figure 1, it is observed that at the point
Also from Figure 1, it is observed that at the point
Thus, the absolute maximum value of
b)
To find: The exact maximum and minimum values of the function
b)
Answer to Problem 57E
The absolute maximum value of
The absolute minimum value of
Explanation of Solution
Obtain the first derivative of the given function.
Differentiate with respect to x.
Set
Here, the critical numbers are
All of the critical numbers lie in the given interval
Apply the extreme values of the given interval and the critical number values in
When
When
When
When
When
Recall the fact that the largest functional value is absolute maximum and smallest functional value is absolute minimum. Compare with above values.
Thus, the absolute maximum value 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