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Consider the function of two variables f(x, y) = 4y√x+3y² and the point P(4, -1). 1. Compute the value of Vf at P. Show your work. 2. Use your answer from part (a) to find the derivative of f at P in the direction of 47+3j. Show your work. 3. Give an example of a non-zero vector w such that the derivative of f at P in the direction of w is 0. Verify your example by showing the derivative is in fact zero in that direction.

Consider the function of two variables f(x, y) = 4y√x+3y² and the point P(4, -1). 1. Compute the value of Vf at P. Show your work. 2. Use your answer from part (a) to find the derivative of f at P in the direction of 47+3j. Show your work. 3. Give an example of a non-zero vector w such that the derivative of f at P in the direction of w is 0. Verify your example by showing the derivative is in fact zero in that direction.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the function of two variables f(x, y) = 4y√x+3y² and the point P(4, -1). 1. Compute the value of Vf at P. Show your work. 2. Use your answer from part (a) to find the derivative of f at P in the direction of 47 +3j. Show your work. 3. Give an example of a non-zero vector w such that the derivative of f at P in the direction of w is 0. Verify your example by showing the derivative is in fact zero in that direction. Note: If you're having difficulty with the last one, start by writing the components of w (a, b) and then writing the equation that you need to make sure this is zero (this should be a fairly simple equation). Then play around with numbers until you find something that fits. There are lots of possibilities, and as long as both a and b aren't zero, then whatever solves your equation works.
Transcribed Image Text:Consider the function of two variables f(x, y) = 4y√x+3y² and the point P(4, -1). 1. Compute the value of Vf at P. Show your work. 2. Use your answer from part (a) to find the derivative of f at P in the direction of 47 +3j. Show your work. 3. Give an example of a non-zero vector w such that the derivative of f at P in the direction of w is 0. Verify your example by showing the derivative is in fact zero in that direction. Note: If you're having difficulty with the last one, start by writing the components of w (a, b) and then writing the equation that you need to make sure this is zero (this should be a fairly simple equation). Then play around with numbers until you find something that fits. There are lots of possibilities, and as long as both a and b aren't zero, then whatever solves your equation works.
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