For the same function f (x, y) as in #1, in what direction should you travel to decrease the value of f (x, y) as quickly as possible? (Hint: v· u = |v||u| cos(0) has its minimum value when 0, the angle between vectors v and u, is π.) For the same function f (x, y) as in #1, in what direction should you travel to keep the value of f(x, y) constant? (Hint: v · u = |v||u| cos(0) is 0 when 0, the angle between vectors v and u, is)

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...
icon
Related questions
Topic Video
Question
100%

please do Q2 and Q3

1. Suppose that f, (0,1) = 3 and fy (0,1) = 2. From the point (0,1), in what direction should you
travel to increase the value of f (x, y) as quickly as possible?
(Hint: v· u = |v||u| cos(0) has its largest value when 0, the angle between vectors v and u, is
0.)
2. For the same function f(x, y) as in #1, in what direction should you travel to decrease the value
of f (x, y) as quickly as possible?
(Hint: v · u =
|v||u| cos(0) has its minimum value when 0, the angle between vectors v and u,
is π.)
3. For the same function f(x, y) as in #1, in what direction should you travel to keep the value of
f (x, y) constant?
(Hint: v · u = |v||u| cos(0) is 0 when 0, the angle between vectors v and u, is .)
Transcribed Image Text:1. Suppose that f, (0,1) = 3 and fy (0,1) = 2. From the point (0,1), in what direction should you travel to increase the value of f (x, y) as quickly as possible? (Hint: v· u = |v||u| cos(0) has its largest value when 0, the angle between vectors v and u, is 0.) 2. For the same function f(x, y) as in #1, in what direction should you travel to decrease the value of f (x, y) as quickly as possible? (Hint: v · u = |v||u| cos(0) has its minimum value when 0, the angle between vectors v and u, is π.) 3. For the same function f(x, y) as in #1, in what direction should you travel to keep the value of f (x, y) constant? (Hint: v · u = |v||u| cos(0) is 0 when 0, the angle between vectors v and u, is .)
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Propositional Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
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