What is the critical x^4+x^2-6xy+3y^2 ?

The critical x^4+x^2-6xy+3y^2 is (0,0),(-1,-1),(1,1)

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critical x^4+x^2-6xy+3y^2

critical points

x^{4} + x^{2} - 6 x y + 3 y^{2}

(0, 0), (- 1, - 1), (1, 1)

Solution steps

x^{4} + x^{2} - 6 x y + 3 y^{2}

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (- 1, - 1), (1, 1)

f (x, y) = 2 x y - \frac{1}{2} (x^{4} + y^{4}) + 1

f (x) = - x^{2} + 3, (- 2 \leq x \leq 3)

f (x) = x^{3} - \frac{2}{3} x^{2}

f (x) = x^{2} + 3 x y + 4 y^{2} - 6 x + 2 y

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

What is the critical x^4+x^2-6xy+3y^2 ?
The critical x^4+x^2-6xy+3y^2 is (0,0),(-1,-1),(1,1)