[10] (3) GIVEN: f(x, y) = 2x² - 6x + 2xy + y² - 2y FIND: a) The set of critical points, A. b) The discriminant of f, A c) Does f have a local minimum? YES d) Does f have a local maximum? YES e) Does f have a saddle point ? YES NO (Box your answer) NO (Box your answer) NO (Box your answer)
[10] (3) GIVEN: f(x, y) = 2x² - 6x + 2xy + y² - 2y FIND: a) The set of critical points, A. b) The discriminant of f, A c) Does f have a local minimum? YES d) Does f have a local maximum? YES e) Does f have a saddle point ? YES NO (Box your answer) NO (Box your answer) NO (Box your 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 attach please do the calculations similar to the second image attach
please please answer every correctly also this is not a graded question I would really appreciate if you would answer
![[10] (3) GIVEN: f(x, y) = 2x² - 6x + 2xy + y²-2y
FIND:
a) The set of critical points, A.
b) The discriminant of f, A
c) Does f have a local minimum? YES
d) Does f have a local maximum ? YES
e) Does f have a saddle point ? YES
NO (Box your answer)
NO (Box your answer)
NO (Box your answer)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa833a647-b9ad-4697-b42a-39aaf6365497%2Fad287160-7d2b-4832-a29a-35a2acba3e21%2Ffufhklb_processed.png&w=3840&q=75)
Transcribed Image Text:[10] (3) GIVEN: f(x, y) = 2x² - 6x + 2xy + y²-2y
FIND:
a) The set of critical points, A.
b) The discriminant of f, A
c) Does f have a local minimum? YES
d) Does f have a local maximum ? YES
e) Does f have a saddle point ? YES
NO (Box your answer)
NO (Box your answer)
NO (Box your answer)
![[10] (3)
GIVEN: f(x, y) = x² - xy + 2y²-x-3y
FIND:
a) The set of critical points, A.
b) The discriminant of f, A
c) Does f have a local minimum ?
d) Does f have a local maximum ?
e) Does f have a saddle point ?
{
(x, y ) € A ⇒ { $ z
fy
YES
-
A =
YES
YES
2x-y-1=0
x + 4y -3 = 0
⇒ A=1
= 0
=
NO (Box your answer)
(Box your answer)
NO
NO (Box your answer)
2-1
0 = | ²₁-4 = 7, 4₂ = | 3 || = 7,4-| ||-7
⇒
(x, y) = (1,1) : A = {(1,1)}
0
fxz fyz - fz²z = (2)(4) − (−1)²
g
> 0
and fxx (1,1)=2>0
χχ
:. f (1,1)= LOC MIN
1
{ 27+45=3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa833a647-b9ad-4697-b42a-39aaf6365497%2Fad287160-7d2b-4832-a29a-35a2acba3e21%2Fcqnhyjpn_processed.png&w=3840&q=75)
Transcribed Image Text:[10] (3)
GIVEN: f(x, y) = x² - xy + 2y²-x-3y
FIND:
a) The set of critical points, A.
b) The discriminant of f, A
c) Does f have a local minimum ?
d) Does f have a local maximum ?
e) Does f have a saddle point ?
{
(x, y ) € A ⇒ { $ z
fy
YES
-
A =
YES
YES
2x-y-1=0
x + 4y -3 = 0
⇒ A=1
= 0
=
NO (Box your answer)
(Box your answer)
NO
NO (Box your answer)
2-1
0 = | ²₁-4 = 7, 4₂ = | 3 || = 7,4-| ||-7
⇒
(x, y) = (1,1) : A = {(1,1)}
0
fxz fyz - fz²z = (2)(4) − (−1)²
g
> 0
and fxx (1,1)=2>0
χχ
:. f (1,1)= LOC MIN
1
{ 27+45=3
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