Concept explainers
To find: The number of hours of daylight increases in Philadelphia on March 21 and May 21.
Answer to Problem 72E
The number of hours of daylight increases in Philadelphia on March 21 and May 21 is approximately 0.0482 and 0.02398.
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),
Apply the chain rule as shown in equation (1),
Let
The derivative of
Substitute
Thus, the derivative is
The derivative of
Thus, the derivative is
Substitute
Therefore, the derivative is
Given that, the rate of the length of daylight is increasing in Philadelphia on March 21 and May 21. That is,
Obtain the value of t for which
Note that,
Here, t is from 21st March to 20 th June.
On March 21, the value of
Substitute
Thus, the number of hours of daylight is increasing in Philadelphia on March 21 is approximately 0.0482.
On May 21, the value of t is
Substitute
Thus, the number of hours of daylight increases in Philadelphia May 21 is approximately 0.02398.
Note:
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