GIVEN: f(x, y) = 2x² - 6x + 2xy + y² - 2y FIND: a) The set of critical points, A. o) 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)
GIVEN: f(x, y) = 2x² - 6x + 2xy + y² - 2y FIND: a) The set of critical points, A. o) 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)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
Related questions
Question
For the first image attached please do the calculations simailar to the second image attached
this is not a graded question
![[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%2Fd94a5c19-4420-43ed-9c79-c568d2a1de91%2F3704caf2-5ee2-4193-987f-e1cc2ee6a59e%2Fat3ykj5_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
A =
YES
-
YES
YES
2x-y-1=0
x + 4y -3=0
⇒ A = 1
=
= 0
0
=
NO (Box your answer)
NO (Box your answer)
NO (Box your answer)
2-1
0 = | ²₁-4 = 7, 4₂ = | 3 || = 7,4-| ||-7
⇒
(x, y) = (1,1) : A = {(1,1)}
2
fxz fyz - fz²z = (2)(4) − (−1)²
g
>0
and fx (1,1)=2>0
xx
:. f (1,1)= LOC MIN
1
{ 27+45=3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd94a5c19-4420-43ed-9c79-c568d2a1de91%2F3704caf2-5ee2-4193-987f-e1cc2ee6a59e%2Fpqf8ywf_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
A =
YES
-
YES
YES
2x-y-1=0
x + 4y -3=0
⇒ A = 1
=
= 0
0
=
NO (Box your answer)
NO (Box your answer)
NO (Box your answer)
2-1
0 = | ²₁-4 = 7, 4₂ = | 3 || = 7,4-| ||-7
⇒
(x, y) = (1,1) : A = {(1,1)}
2
fxz fyz - fz²z = (2)(4) − (−1)²
g
>0
and fx (1,1)=2>0
xx
:. f (1,1)= LOC MIN
1
{ 27+45=3
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