To show : the curves are orthogonal to indicated points.
Explanation of Solution
Given information :
The curves are
Formula needed :
Chain rule of derivative:
Product rule of derivative:
The product of slopes is
For slope, differentiate
Substitute
The slope at point
Substitute
The slope at point
For slope, differentiate
Substitute
The slope at point
Substitute
The slope at point
The product of
The product of
Hence, the curves are orthogonal to each other at points
Chapter 3 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
- 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