Can you show the baby steps of how to get from the circled part to the squared part. lost on how they computed the vector. 8. Letf(x, y, z) = In (x² + y² – 1) + y + 6z.In what direction ī is f(x, y, z) increasing most rapidly at the point (1, 1, 0)?Give your answer as a unit vector ū. What is the directional derivative of fin the direction u?Solution.• We have2x2yVf(x, y, z) =(x² + y² – 1x² + y?+1)5+6k,1ThusVf(1,1,0) = 27+ 37+ 6k.• The function f is most rapidly increasing in the directionVf|Vf|(27 +33+ 6k) .• The directional derivative of f in the direction u isdf= |Vf| = 7.

We have to show the steps for the above equation.

Answered: • We have 2x 2y Vf(x, y, z) = i+…

Math

Calculus

• We have 2x 2y Vf(x, y, z) = i+ +1)j+6k. x² + y²- 1 x² + y? – 1 | Thus Vf(1,1,0) = 27 + 37 + 6K.

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...

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Question

Can you show the baby steps of how to get from the circled part to the squared part. lost on how they computed the vector.

8. Let
f(x, y, z) = In (x² + y² – 1) + y + 6z.
In what direction ī is f(x, y, z) increasing most rapidly at the point (1, 1, 0)?
Give your answer as a unit vector ū. What is the directional derivative of f
in the direction u?
Solution.
• We have
2x
2y
Vf(x, y, z) =
(x² + y² – 1
x² + y?
+1)5+6k,
1
Thus
Vf(1,1,0) = 27+ 37+ 6k.
• The function f is most rapidly increasing in the direction
Vf
|Vf|
(27 +33+ 6k) .
• The directional derivative of f in the direction u is
df
= |Vf| = 7.

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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