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

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

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

critical points

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

(4, 0), (0, 0), (2, 2), (2, - 2)

Solution steps

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

Find where

\nabla f (y, x)

is equal to zero or undefined

(4, 0), (0, 0), (2, 2), (2, - 2)

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

f (x) = 5 - 2 x^{2} + 3 x^{3} - x^{4}

f (x) = x^{2} - 8 ln (7 x)

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

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

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