a.
To find: The slope of the curve
a.
Answer to Problem 21E
Explanation of Solution
Given information:
The function is
Concept used:
For any function f , slope at any point
Calculation:
Let
For
The slope of the function is
b.
To find: what happens to the slope if the value of a changes.
b.
Answer to Problem 21E
The slope of the tangent will always be negative and the tangent will be very steep near
Explanation of Solution
Given information:
The function is
Calculation:
From part (a) it was found that the slope of the tangent is
The slope will always be negative.
The behavior of the slope depends on the value of a .
In an expression like
Also, the tangent will be very steep near
Conclusion:
The slope of the tangent increases as a increases and will always be negative
Chapter 1 Solutions
CALCULUS-W/XL ACCESS
- 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