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

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

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

critical points

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

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

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

(x - 2) (x - 3)^{2}

f (x) = \frac{1}{3} x^{3} - \frac{5}{2} x^{2} + 6 x + 8

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

\frac{3 x + 2}{x ^{2}}

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