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(a)Find the critical point of f(x,y)=(2x²-y) (x²+4y) (x,y)=_ (b) Find the discriminant, D(x,y) for the function D(x,y)=_

(a)Find the critical point of f(x,y)=(2x²-y) (x²+4y) (x,y)=_ (b) Find the discriminant, D(x,y) for the function D(x,y)=_

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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(a)Find the critical point of f(x,y)=(2x²-y) (x²+4y) (x,y)= (b) Find the discriminant, D(x,y) for the function D(x,y)=_ what is the value of the discriminant at the critical point? D= What does this tell us about the critical point? (c)Sketch contours near the critical point to determine, or confirm, whether it is a local maximum, a local minimum, a saddle point, or none of these.
Transcribed Image Text:(a)Find the critical point of f(x,y)=(2x²-y) (x²+4y) (x,y)= (b) Find the discriminant, D(x,y) for the function D(x,y)=_ what is the value of the discriminant at the critical point? D= What does this tell us about the critical point? (c)Sketch contours near the critical point to determine, or confirm, whether it is a local maximum, a local minimum, a saddle point, or none of these.
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