a) What is the rate of change of f(x, y) = 3xy + y^2 at the point (2, 4) in the direction of vector v = -3i - j? b) What is the direction of maximum rate of change of f at (2, 4)? c) What is the maximum rate of change?

a) What is the rate of change of f(x, y) = 3xy + y^2 at the point (2, 4) in the direction of vector v = -3i - j? b) What is the direction of maximum rate of change of f at (2, 4)? c) What is the maximum rate of change?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 39RE

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Question

a) What is the rate of change of f(x, y) = 3xy + y^2 at the point (2, 4) in the direction of vector v = -3i - j?

b) What is the direction of maximum rate of change of f at (2, 4)?

c) What is the maximum rate of change?

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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