Function: h(x, y) = 9y cos (x - y) (0. E) Point: (a) Find the gradient of the function. -9y sin (x – y) i+ 9 cos(x- y) + 9y sin(x – y) j (b) Find the maximum value of the directional derivative at the given point. (Give your answer correct to 2 decimal places.
Function: h(x, y) = 9y cos (x - y) (0. E) Point: (a) Find the gradient of the function. -9y sin (x – y) i+ 9 cos(x- y) + 9y sin(x – y) j (b) Find the maximum value of the directional derivative at the given point. (Give your answer correct to 2 decimal places.
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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![Consider the following.
Function: \( h(x, y) = 9y \cos(x-y) \)
Point: \( \left( 0, \frac{\pi}{3} \right) \)
(a) Find the gradient of the function.
Gradient:
\[
\left[ -9y \sin(x-y) \right] \mathbf{i} + \left[ 9 \cos(x-y) + 9y \sin(x-y) \right] \mathbf{j}
\]
(b) Find the maximum value of the directional derivative at the given point. (Give your answer correct to 2 decimal places.)
Answer box: [ ] (incorrect attempt)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b6a8b4b-7f8b-457c-9250-505f0d43a556%2Fd00e4627-e091-4db4-a781-579c324abcf3%2Fi1il0b_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following.
Function: \( h(x, y) = 9y \cos(x-y) \)
Point: \( \left( 0, \frac{\pi}{3} \right) \)
(a) Find the gradient of the function.
Gradient:
\[
\left[ -9y \sin(x-y) \right] \mathbf{i} + \left[ 9 \cos(x-y) + 9y \sin(x-y) \right] \mathbf{j}
\]
(b) Find the maximum value of the directional derivative at the given point. (Give your answer correct to 2 decimal places.)
Answer box: [ ] (incorrect attempt)
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