Consider the function. f(x, y) = 6 – -% 5 4 Find Duf(7, 6), where u = cos(0)i + sin(0)j. (a) 0 = 4 %3D Duf(7, 6) = 2n (b) %D 3 Duf(7, 6) (c) = %3D Duf(7, 6) = IT (b) = %3D 6
Consider the function. f(x, y) = 6 – -% 5 4 Find Duf(7, 6), where u = cos(0)i + sin(0)j. (a) 0 = 4 %3D Duf(7, 6) = 2n (b) %D 3 Duf(7, 6) (c) = %3D Duf(7, 6) = IT (b) = %3D 6
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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![### Gradient Evaluation Problem
Consider the function:
\[ f(x, y) = 6 - \frac{x}{5} - \frac{y}{4} \]
Find \( D_{\mathbf{u}}f(7, 6) \), where \( \mathbf{u} = \cos(\theta)\mathbf{i} + \sin(\theta)\mathbf{j} \).
#### Compute the Directional Derivative for:
(a) \( \theta = \frac{\pi}{4} \)
\[ D_{\mathbf{u}}f(7, 6) = \boxed{\phantom{0}} \]
(b) \( \theta = \frac{2\pi}{3} \)
\[ D_{\mathbf{u}}f(7, 6) = \boxed{\phantom{0}} \]
(c) \( \theta = \frac{4\pi}{3} \)
\[ D_{\mathbf{u}}f(7, 6) = \boxed{\phantom{0}} \]
(d) \( \theta = -\frac{\pi}{6} \)
\[ D_{\mathbf{u}}f(7, 6) = \boxed{\phantom{0}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fa7ac50-e43d-4267-956c-145cd19bd43c%2F1e6f33b3-109d-4a76-97c3-7bc1ae99207a%2Fl55cxy_processed.png&w=3840&q=75)
Transcribed Image Text:### Gradient Evaluation Problem
Consider the function:
\[ f(x, y) = 6 - \frac{x}{5} - \frac{y}{4} \]
Find \( D_{\mathbf{u}}f(7, 6) \), where \( \mathbf{u} = \cos(\theta)\mathbf{i} + \sin(\theta)\mathbf{j} \).
#### Compute the Directional Derivative for:
(a) \( \theta = \frac{\pi}{4} \)
\[ D_{\mathbf{u}}f(7, 6) = \boxed{\phantom{0}} \]
(b) \( \theta = \frac{2\pi}{3} \)
\[ D_{\mathbf{u}}f(7, 6) = \boxed{\phantom{0}} \]
(c) \( \theta = \frac{4\pi}{3} \)
\[ D_{\mathbf{u}}f(7, 6) = \boxed{\phantom{0}} \]
(d) \( \theta = -\frac{\pi}{6} \)
\[ D_{\mathbf{u}}f(7, 6) = \boxed{\phantom{0}} \]
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