[15] (2) Consider the function ƒ: R² → R, ƒ(x, y) = x² − 2xy + 2y² Determine Vf. a) b) c) GIVEN: The point Po (2,1) and the vector a (2, 2). Determine the directional derivative of ƒ at P, in the direction of a. = = Consider the point Po (2,1) Determine the maximum value of the directional derivative at Po. =
[15] (2) Consider the function ƒ: R² → R, ƒ(x, y) = x² − 2xy + 2y² Determine Vf. a) b) c) GIVEN: The point Po (2,1) and the vector a (2, 2). Determine the directional derivative of ƒ at P, in the direction of a. = = Consider the point Po (2,1) Determine the maximum value of the directional derivative at Po. =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
For the first image attached please do the calculations simailar to the second image attached
try to answer similar to the second image attached please
![[15] (2)
a)
b)
c)
Consider the function f: R²R, f(x, y):
=
Determine Vf.
⇒ Vf
d)
x² - 4xy + y²
GIVEN: The point P, = (2,1) and the vector a = (1,2).
Determine the directional derivative of f at Po in the direction of a.
:. [D₂f|(21) = 4(7,-1)+ (1,2),
=
√5
4x³− 4y, −4x + 4
−x
Vf = 4(x³-y, -x + y³)
⇒ Vf (2,1)= 4(7, -1)
MAX Df|(2,1)
Consider the point Po = (2,1)
Determine the maximum value of the directional derivative at Po.
4.5
√5
4y³)
At the point Po
(2,1),
is there a direction so that the directional derivative is 9√5?
YES NO
(box correct answer)
-20√2 <9√√5 ≤ 20√2
<
=
|| 4 (7,-1)|| = 4|| (7,-1) ||
= 4√50 = 20√√2
= 4√5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F092645f9-ebb0-43ba-b170-38d39101f7b1%2F2e94e063-8d25-4576-9c35-cd52d9eb3c63%2F4snih_processed.png&w=3840&q=75)
Transcribed Image Text:[15] (2)
a)
b)
c)
Consider the function f: R²R, f(x, y):
=
Determine Vf.
⇒ Vf
d)
x² - 4xy + y²
GIVEN: The point P, = (2,1) and the vector a = (1,2).
Determine the directional derivative of f at Po in the direction of a.
:. [D₂f|(21) = 4(7,-1)+ (1,2),
=
√5
4x³− 4y, −4x + 4
−x
Vf = 4(x³-y, -x + y³)
⇒ Vf (2,1)= 4(7, -1)
MAX Df|(2,1)
Consider the point Po = (2,1)
Determine the maximum value of the directional derivative at Po.
4.5
√5
4y³)
At the point Po
(2,1),
is there a direction so that the directional derivative is 9√5?
YES NO
(box correct answer)
-20√2 <9√√5 ≤ 20√2
<
=
|| 4 (7,-1)|| = 4|| (7,-1) ||
= 4√50 = 20√√2
= 4√5
![[15] (2) Consider the function f: R² → R, f(x, y) = x² − 2xy + 2y²
Determine Vf.
a)
b)
c)
d)
GIVEN: The point Po
(2,1) and the vector a
(2, 2).
Determine the directional derivative of fat Po in the direction of a.
=
=
Consider the point Po
(2,1)
Determine the maximum value of the directional derivative at Po.
=
At the point Po
(2,1),
is there a direction so that the directional derivative is 3?
YES
NO
(box correct answer)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F092645f9-ebb0-43ba-b170-38d39101f7b1%2F2e94e063-8d25-4576-9c35-cd52d9eb3c63%2Fczrajwm_processed.png&w=3840&q=75)
Transcribed Image Text:[15] (2) Consider the function f: R² → R, f(x, y) = x² − 2xy + 2y²
Determine Vf.
a)
b)
c)
d)
GIVEN: The point Po
(2,1) and the vector a
(2, 2).
Determine the directional derivative of fat Po in the direction of a.
=
=
Consider the point Po
(2,1)
Determine the maximum value of the directional derivative at Po.
=
At the point Po
(2,1),
is there a direction so that the directional derivative is 3?
YES
NO
(box correct answer)
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