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

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

6 x^{2} - x^{3}

\frac{x}{x ^{2} + 9}

x (1 - x^{2})^{2}

f (x, y) = x y + \frac{8}{x} + \frac{8}{y}

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

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