What is the critical f(x)=x^3-3x^2+y^3-3y ?

The critical f(x)=x^3-3x^2+y^3-3y is (0,1),(0,-1),(2,1),(2,-1)

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critical f(x)=x^3-3x^2+y^3-3y

critical points

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

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

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

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

x + 4 y + \frac{2}{x y}

3 x^{4} - 2 x^{3} + 1

x^{4} + 6 x^{3} - 5 x^{2} + 2 x + 3

\frac{x - 3}{x - 5}

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

What is the critical f(x)=x^3-3x^2+y^3-3y ?
The critical f(x)=x^3-3x^2+y^3-3y is (0,1),(0,-1),(2,1),(2,-1)