To show: The x value halfway between the x-coordinate p and q.
Explanation of Solution
Given:
The equation of the parabola is
Formula used:
The equation of the tangent line at
Where, m is the slope of the tangent line at
Proof:
Consider the function
Differentiate with respect to x,
Thus, the derivative of the equation is
Substitute
Substitute
That is, the slope of tangent to the equation is,
Substitute
Substitute
Equating equation (2) and equation (3),
Simplify further,
Hence the required proof is obtained.
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