Homework Help is Here – Start Your Trial Now!
Math
Calculus
2. Let f(r, y) be a differentiable real valued function in two variables. If Vf (z0 m) = (f (ro, yo). fy(ro. yo)), then using the fact that the gradient is orthogonal to the level curve, show that the tangent line through the level curve of f through (ro, yo) is given by the equation fz(To, Yo)(x- 0) + f,(ro, Yo)(y-yo) = 0.

2. Let f(r, y) be a differentiable real valued function in two variables. If Vf (z0 m) = (f (ro, yo). fy(ro. yo)), then using the fact that the gradient is orthogonal to the level curve, show that the tangent line through the level curve of f through (ro, yo) is given by the equation fz(To, Yo)(x- 0) + f,(ro, Yo)(y-yo) = 0.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
answer quickly
2. Let f(r, y) be a differentiable real valued function in two variables. If Vfl(ro:0) = (f(ro: yo), fy(r0: y0)), then using the fact that the gradient is orthogonal to the level curve, show that the tangent line through the level curve of f through (ro, yo) is given by the equation fa (To, Yo)(x - 1o) + fy(To, Yo)(y- yo) = 0.
Transcribed Image Text:2. Let f(r, y) be a differentiable real valued function in two variables. If Vfl(ro:0) = (f(ro: yo), fy(r0: y0)), then using the fact that the gradient is orthogonal to the level curve, show that the tangent line through the level curve of f through (ro, yo) is given by the equation fa (To, Yo)(x - 1o) + fy(To, Yo)(y- yo) = 0.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS