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

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

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

critical points

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

(0, 2), (- 1, 2), (1, 2)

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 2), (- 1, 2), (1, 2)

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

f (x) = x^{3} - 9 x^{2} + 24 x - 7

f (x) = x^{2} - 2 x y + 2 y^{2} + 4 x - 8 y + 24

f (x) = \frac{x}{( 1 - x )}

f (x) = I n (x - 2)

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