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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)

Advanced Engineering Mathematics
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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For the first image attached please do the calculations simailar to the second image attached

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[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)
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
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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