What is the critical f(x,y)=x^4+y^4-2x^2+4xy-2y^2 ?

The critical f(x,y)=x^4+y^4-2x^2+4xy-2y^2 is (0,0),(-sqrt(2),sqrt(2)),(sqrt(2),-sqrt(2))

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critical f(x,y)=x^4+y^4-2x^2+4xy-2y^2

critical points

f (x, y) = x^{4} + y^{4} - 2 x^{2} + 4 x y - 2 y^{2}

(0, 0), (- 2, 2), (2, - 2)

Solution steps

x^{4} + y^{4} - 2 x^{2} + 4 x y - 2 y^{2}

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (- 2, 2), (2, - 2)

f (x) = x^{3} - 3 x^{2} + 4

f (x) = 2 x^{2} - 8 x + 9

f (x) = x^{3} + 3 x^{2} + 1

f (x) = sin^{2} (x) + cos (x), 0 < x < 2 π

f (x, y) = 4 x y - x^{4} - 2 y^{2} + 2

What is the critical f(x,y)=x^4+y^4-2x^2+4xy-2y^2 ?
The critical f(x,y)=x^4+y^4-2x^2+4xy-2y^2 is (0,0),(-sqrt(2),sqrt(2)),(sqrt(2),-sqrt(2))