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

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

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

critical points

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

(0, 3), (0, - 1), (\frac{2}{3}, 1), (- \frac{2}{3}, 1)

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 3), (0, - 1), (\frac{2}{3}, 1), (- \frac{2}{3}, 1)

x^{2} + 4 x + 4

f (x) = \frac{x}{x ^{2} - 9}

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

f (x, y) = x^{4} + y^{4} + 6 x^{2} y^{2} + 8 x^{3}

x^{4} - 4 x^{3} + 7

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