Concept explainers
(a)
To find: The given function can have two, one or no critical numbers.
(a)
Answer to Problem 66E
The function can have two, one or no critical numbers is proved.
Explanation of Solution
Given information:
The given function is
Calculation:
Calculate
This is a quadratic equation which can have two, one or no real roots.
Therefore, the function
Figure (1)
Figure (2)
Figure (3)
Therefore, the function can have two, one or no critical numbers is proved.
(b)
To find: The number of local extreme of a cubic function.
(b)
Answer to Problem 66E
The cubic function has no local extreme value.
Explanation of Solution
Given information:
The given function is
Calculation:
Using part (a), we see that a cubic function can have at most two local extreme values it depends on the number of critical numbers, if the cubic function has only one critical number or no critical number then there is no local extreme value.
Therefore, the cubic function has no local extreme value.
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