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Consider the function f(x,y) %— ху — х -4 у a) The critical point of f is (х,у)- (4,1) b) According to the second derivative test, the critical point found in part a) yields A. saddle point B. local minimum C. inconclusive D. local maximum c) Consider the function f restricted to the region on the xy plane bounded by the triangle with vertices (0,4), (4,0) and (8,4). What is the absolute maximum and absolute minimum f takes on this region? Absolute max = 16 - 8 and occurs at the point ( 8', 4') Absolute min = - 16 and occurs at the point ( 0 , 4')

Consider the function f(x,y) %— ху — х -4 у a) The critical point of f is (х,у)- (4,1) b) According to the second derivative test, the critical point found in part a) yields A. saddle point B. local minimum C. inconclusive D. local maximum c) Consider the function f restricted to the region on the xy plane bounded by the triangle with vertices (0,4), (4,0) and (8,4). What is the absolute maximum and absolute minimum f takes on this region? Absolute max = 16 - 8 and occurs at the point ( 8', 4') Absolute min = - 16 and occurs at the point ( 0 , 4')

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 39RE
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Consider the function f(x,y) — ху — х - 4 у a) The critical point of f is (ху)- (4,1) b) According to the second derivative test, the critical point found in part a) yields A. saddle point B. local minimum CC. inconclusive D. local maximum c) Consider the function f restricted to the region on the xy plane bounded by the triangle with vertices (0,4), (4,0) and (8,4). What is the absolute maximum and absolute minimum f takes on this region? Absolute max = 16 - 8 and occurs at the point ( 8', 4) Absolute min = - 16 and occurs at the point ( 0, 4)
Transcribed Image Text:Consider the function f(x,y) — ху — х - 4 у a) The critical point of f is (ху)- (4,1) b) According to the second derivative test, the critical point found in part a) yields A. saddle point B. local minimum CC. inconclusive D. local maximum c) Consider the function f restricted to the region on the xy plane bounded by the triangle with vertices (0,4), (4,0) and (8,4). What is the absolute maximum and absolute minimum f takes on this region? Absolute max = 16 - 8 and occurs at the point ( 8', 4) Absolute min = - 16 and occurs at the point ( 0, 4)
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