Exercise 3: Rate of Change of a Nonlinear Function in Direction U a) Estimate the directional derivative at the indicated point in the indicated direction by measuring a small change in displacement and the corresponding change in z. 4 L 2 0 4 =2 1 N 3 1 6 7 5 3 2 4 4 2 0 2 4 b) For the function f[x, y] = 8-2-2 4y², calculate the directional derivative of the function at (x, y) = (3,3√3) 4 9 in the direction of the vector V = A 2 2 Sketch the gradient on the figure of part (a). 3
Exercise 3: Rate of Change of a Nonlinear Function in Direction U a) Estimate the directional derivative at the indicated point in the indicated direction by measuring a small change in displacement and the corresponding change in z. 4 L 2 0 4 =2 1 N 3 1 6 7 5 3 2 4 4 2 0 2 4 b) For the function f[x, y] = 8-2-2 4y², calculate the directional derivative of the function at (x, y) = (3,3√3) 4 9 in the direction of the vector V = A 2 2 Sketch the gradient on the figure of part (a). 3
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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![Exercise 3: Rate of Change of a Nonlinear Function in Direction U
a) Estimate the directional derivative at the indicated point in the indicated direction by measuring a small
change in displacement and the corresponding change in z.
4 L
2
0
4
=2
1
N
3
1
6
7
5
3
2
4
4
2
0
2
4
b) For the function f[x, y] = 8-2-2
4y², calculate the directional derivative of the function at
(x, y) = (3,3√3)
4
9
in the direction of the vector V =
A
2
2
Sketch the gradient on the figure of part (a).
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ab8c171-06b2-4efe-a843-f730abff628e%2Fbf776751-31a6-4a5a-92a2-befc5496c68f%2Fflp8c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 3: Rate of Change of a Nonlinear Function in Direction U
a) Estimate the directional derivative at the indicated point in the indicated direction by measuring a small
change in displacement and the corresponding change in z.
4 L
2
0
4
=2
1
N
3
1
6
7
5
3
2
4
4
2
0
2
4
b) For the function f[x, y] = 8-2-2
4y², calculate the directional derivative of the function at
(x, y) = (3,3√3)
4
9
in the direction of the vector V =
A
2
2
Sketch the gradient on the figure of part (a).
3
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