Consider the function ƒ: R² → R, f(x, y) = x² − 2xy + 2y² Determine Vf. GIVEN: The point Po (2, 1) and the vector a = (2, 2). Determine the directional derivative of f at P. 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)
Consider the function ƒ: R² → R, f(x, y) = x² − 2xy + 2y² Determine Vf. GIVEN: The point Po (2, 1) and the vector a = (2, 2). Determine the directional derivative of f at P. 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)
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
For the first image attached please do the calculations similar to the second image
![[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%2Fd94a5c19-4420-43ed-9c79-c568d2a1de91%2Fe6f74626-4369-44d1-a6a1-6e5c3ecbccc0%2Fpnnoc7w_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)
![[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%2Fd94a5c19-4420-43ed-9c79-c568d2a1de91%2Fe6f74626-4369-44d1-a6a1-6e5c3ecbccc0%2F7lnnpwh_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
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