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

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

critical points

f (x) = 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) = y^{2} - y

\frac{x}{x ^{2} + 16 x + 60}

f (x) = 6 x^{3} - 15 x^{2} + 12 x - 6

f (x, y) = e^{y} - y e^{x}

f (x, y) = \frac{x}{y} + \frac{8}{x} - y

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