Concept explainers
(a)
To find: The rate of change of the brightness after t days.
(a)
Answer to Problem 71E
The rate of change of the brightness after t days is
Explanation of Solution
Given:
The function
Derivative rule:
(1) Constant Multiple Rule:
(2)
(3)
Result used: Chain Rule
If g is differentiable at x and f is differentiable at
Calculation:
Obtain the derivative of
Apply the sum rule (1) and the constant multiple rule (2),
Obtain the derivative
Let
The derivative of
Substitute
Thus, the derivative is
The derivative of
Thus, the derivative is
Substitute
Substitute
Therefore, the rate of change of the brightness after t days is
(b)
To find: The rate of increase after one day and correct to two decimal places.
(b)
Answer to Problem 71E
The rate of increase after one day is
Explanation of Solution
Calculation:
From part (a), the rate of change of the brightness after t days is
Substitute
Therefore, the rate of increase after one day is
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