Use the contour diagram for f(x, y) shown below to estimate the directional derivative of f in the direction v at the point P.

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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Question
Use the contour diagram for f(x, y) shown below to
estimate the directional derivative of f in the direction v
at the point P.
(a) At the point P = (2, 2) in the direction v = j, the
directional derivative is approximately
(b) At the point P = (2,3) in the direction=-7, the
directional derivative is approximately
D
(c) At the point P = (4, 1) in the direction.
v = (i+j)/√2, the directional derivative is
approximately
(d) At the point P = (4,0) in the direction v = −ỉ, the
directional derivative is approximately
Transcribed Image Text:Use the contour diagram for f(x, y) shown below to estimate the directional derivative of f in the direction v at the point P. (a) At the point P = (2, 2) in the direction v = j, the directional derivative is approximately (b) At the point P = (2,3) in the direction=-7, the directional derivative is approximately D (c) At the point P = (4, 1) in the direction. v = (i+j)/√2, the directional derivative is approximately (d) At the point P = (4,0) in the direction v = −ỉ, the directional derivative is approximately
4.8
y
4
3.2
2.4
1.6
0.8
0.0
2.0
0
-0.8
-0.8
4.0
2.0
아 -0.0
6.0
18.0
16.0
14.0
12.0
10.0
0.8
1.6
x
8.0
2.0
2.4
3.2
4
4.8
Transcribed Image Text:4.8 y 4 3.2 2.4 1.6 0.8 0.0 2.0 0 -0.8 -0.8 4.0 2.0 아 -0.0 6.0 18.0 16.0 14.0 12.0 10.0 0.8 1.6 x 8.0 2.0 2.4 3.2 4 4.8
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