Find Critical point and nature f(x,y)=(x^2+y^2)^2−2x^2+2y^2 So (del)/(delx)f(x,y)=4x(x^2+y^2)−4x (del)/(del)yf(x,y)=4y(x^2+y^2)+4y

allucinemsj 2022-08-09 Answered
Find Critical point and nature
4 x ( x 2 + y 2 1 ) = 0
4 y ( x 2 + y 2 + 1 ) = 0
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Answers (1)

Evelin Castillo
Answered 2022-08-10 Author has 12 answers
From the second equation, y = 0. That's because
x 2 + y 2 + 1 1
for any real x and y. So than either x = 0 or x 2 1 = 0. So the critical points are ( 0 , 0 ), ( 1 , 0 ), and ( 1 , 0 ).
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