Concept explainers
To find:the point P on the arc AOB of the parabola that maximizes the area of the triangle PAB.
Answer to Problem 17P
The pointPonthearcAOBoftheparabola is
Explanation of Solution
Given information:
The givenline is,
Intersects theparabola
Concept used:
The quadraticequationis
Bythequadraticequation
Thepoint
Set
Theareasofthreetrapezoidsare
Bycalculated,
Todifferentiatetheequationwithrespectto
To differentiate the equation again with respect to
Since
Simplified as,
Simplify further,
By the quadratic equation
By the quadratic equation
TheareaofthetrianglePABis
Therefore, thepoint P on the arc AOB of the parabola is
Chapter 4 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