Concept explainers
(a)
To show: The function
(a)
Explanation of Solution
Given:
The function is
Proof:
Obtain the derivative of the function
Differentiate implicitly with respect to x,
Here, the value
Note that, if
Thus,
Therefore, the function
Hence the required result is proved.
(b)
To find: The values of
(b)
Answer to Problem 54E
The value
Explanation of Solution
Calculation:
Obtain the value of
Let
Substitute
Thus, the value is
Since
Therefore, the value
(c)
To find: The value of the
(c)
Answer to Problem 54E
The value
Explanation of Solution
Formula used:
The derivative of inverse function
Calculation:
Given function is
Substitute 1 for x in
From part (a) and (b), the derivative is
Substitute 0 for x in
Thus, the value is
Substitute
Therefore, the value
Chapter 3 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