What is the critical f(x)=x^2y+y^3-12y ?

The critical f(x)=x^2y+y^3-12y is (0,2),(0,-2),(2sqrt(3),0),(-2sqrt(3),0)

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critical f(x)=x^2y+y^3-12y

critical points

f (x) = x^{2} y + y^{3} - 12 y

(0, 2), (0, - 2), (23, 0), (- 23, 0)

Solution steps

x^{2} y + y^{3} - 12 y

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 2), (0, - 2), (23, 0), (- 23, 0)

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

f (x, y) = - 11 + 17 x^{2} + x y + y^{2}

f (x) = \frac{x - 3}{x ^{2} - 5 x + 6}

\frac{1}{2} x^{4} - 3 x y + 3 y^{4}

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

What is the critical f(x)=x^2y+y^3-12y ?
The critical f(x)=x^2y+y^3-12y is (0,2),(0,-2),(2sqrt(3),0),(-2sqrt(3),0)