Find the critical points of a function f(x,y)=xy^{2}-3x^{2}-y^{2}-2x+2

Monique Slaughter 2021-12-16 Answered
Find the critical points of a function f(x,y)=xy23x2y22x+2
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Wendy Boykin
Answered 2021-12-17 Author has 35 answers
Partial derivatives of z=f(x,y)=xy23x2y22x+2 are zx=y26x+2 and zy=2xy2y=2y(x1)
Make them equal to zero to find the critical points: y26x+2=0,2y(x1)=0
The second equation will be true when y=0, then the first equation will be 6x+2=0 so that 6x=2 and x=13. Now, we have one critical point: (x,y)=(13,0)
The second equation wiil also be true when x=1. Then, the first equation will be y24=0 and y2=4, making y=±2. Now, we have two critical points: (x,y)=(1,2) and (x,y)=(1,2)
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Shannon Hodgkinson
Answered 2021-12-18 Author has 34 answers

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