What is the critical f(x,y)=y^4+4x^2y^2-2y^2+2x^2-1 ?

The critical f(x,y)=y^4+4x^2y^2-2y^2+2x^2-1 is (0,0),(0,-1),(0,1)

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critical f(x,y)=y^4+4x^2y^2-2y^2+2x^2-1

critical points

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

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

Solution steps

y^{4} + 4 x^{2} y^{2} - 2 y^{2} + 2 x^{2} - 1

Find where

\nabla f (x, y)

is equal to zero or undefined

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

f (x) = 120 x^{2} - 2 x^{3}

f (x) = \frac{x}{- 2 - ln ( x )}

f (x) = x^{\frac{2}{3}} (x^{2} - 1)

y = \frac{x - 3}{x ^{2} - 3 x + 9}

f (x) = - 2 csc (3 x + π) - 1

What is the critical f(x,y)=y^4+4x^2y^2-2y^2+2x^2-1 ?
The critical f(x,y)=y^4+4x^2y^2-2y^2+2x^2-1 is (0,0),(0,-1),(0,1)