To determine the point on the graph at which the function is increasing most rapidly using the graph of the function.
Answer to Problem 103E
The point on the graph at which the function is increasing most rapidly is
Explanation of Solution
Given:
The total revenue
And the graph of the above function is shown below
Point of diminishing returns is a point in the graph at which return per unit expense is maximum. Return after this point will decrease for each dollar spent on advertisement. That means rate of increase of the return is to be maximized.
So find the second derivative of the function and equate to 0.
Points found out in this way is the point at which rate is maximum.
So differentiate the function,
The point on the graph at which the function is increasing most rapidly is
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
- 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