5] (2) Consider the function f: R²R, f(x, y) = x² - 2xy + 2y² Determine Vf. (2, 2). GIVEN: The point Po Determine the directional derivative of f at P, in the direction of (2,1) and the vector a =
5] (2) Consider the function f: R²R, f(x, y) = x² - 2xy + 2y² Determine Vf. (2, 2). GIVEN: The point Po Determine the directional derivative of f at P, in the direction of (2,1) and the vector a =
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
use the first image attached as reference/example to do the calculations for the second image attached
![[15] (2)
a)
b)
c)
Consider the function f:R²R, f(x, y)
=
Determine Vf.
d)
x² - 4xy + y²
3
⇒ Vƒ = (4x³. 4y, - 4x + 4y³)
GIVEN: The point Po= (2,1) and the vector a = (1,2).
Determine the directional derivative of f at Po in the direction of a.
:. [D_.f|(2,1) = 4(7,-1)• (1,2) – 4-5 - 4√5′
=
3
Vf = 4(x²-y, -x + y ³)
⇒Vƒ (2,1) = 4(7, -1)
Consider the point Po = (2,1)
Determine the maximum value of the directional derivative at Po.
MAX Df | (2, 1) = || 4 (7,-1)|| = 4 ||(7,-1) ||
+√√50 = 2012
=
At the point P = (2,1),
is there a direction so that the directional derivative is 9√5?
(box correct answer)
YES
NO
-20√2 <9√5 ≤ 20√2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F767da4a8-c644-4919-9393-25d8fa6c982f%2F1a335835-c85a-4583-9dad-13b005efc72b%2Fc4xx66_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[15] (2)
a)
b)
c)
Consider the function f:R²R, f(x, y)
=
Determine Vf.
d)
x² - 4xy + y²
3
⇒ Vƒ = (4x³. 4y, - 4x + 4y³)
GIVEN: The point Po= (2,1) and the vector a = (1,2).
Determine the directional derivative of f at Po in the direction of a.
:. [D_.f|(2,1) = 4(7,-1)• (1,2) – 4-5 - 4√5′
=
3
Vf = 4(x²-y, -x + y ³)
⇒Vƒ (2,1) = 4(7, -1)
Consider the point Po = (2,1)
Determine the maximum value of the directional derivative at Po.
MAX Df | (2, 1) = || 4 (7,-1)|| = 4 ||(7,-1) ||
+√√50 = 2012
=
At the point P = (2,1),
is there a direction so that the directional derivative is 9√5?
(box correct answer)
YES
NO
-20√2 <9√5 ≤ 20√2
![[15] (2) Consider the function ƒ: R² → R, ƒ(x, y) = x² − 2xy + 2y²
Determine Vf.
a)
b)
c)
d)
GIVEN: The point Po
(2,1) and the vector a =
Determine the directional derivative of f at P, in the direction of a.
=
a = (2, 2).
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%2F767da4a8-c644-4919-9393-25d8fa6c982f%2F1a335835-c85a-4583-9dad-13b005efc72b%2Ffp0k3p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[15] (2) Consider the function ƒ: R² → R, ƒ(x, y) = x² − 2xy + 2y²
Determine Vf.
a)
b)
c)
d)
GIVEN: The point Po
(2,1) and the vector a =
Determine the directional derivative of f at P, in the direction of a.
=
a = (2, 2).
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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