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

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

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

critical points

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

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

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

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

f (x) = 3 x + \frac{108}{x}

2 x^{3} - 39 x^{2} + 180 x + 6

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

f (x) = x^{3} - I n (x (x^{2} + 1))

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

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