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

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

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

critical points

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

(1, 0), (- 3, 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

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

\frac{1}{x} - ln (x)

y = x 4 - x^{2}

f (x) = 4 x^{2} - 128 x

f (x) = x^{\frac{1}{3}}

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

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