Answered: Find the direction in which the maximum…

Find the direction in which the maximum rate of change occurs for the function f ( x , y ) = 3 x sin ( x y ) at the point (4,3). Give your answer as a unit vector.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.CR: Chapter 4 Review

Problem 3CR: Determine whether each of the following statements is true or false, and explain why. The derivative...

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Question

Find the direction in which the maximum rate of change occurs for the function f ( x , y ) = 3 x sin ( x y ) at the point (4,3). Give your answer as a unit vector.

For the function f ( x , y ) = − 3 e^ 5 x sin ( y ) , find a unit tangent vector to the level curve at the point ( − 5 , 5 ) that has a positive x component. Present your answer with three decimal places of accuracy.

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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