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

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

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

critical points

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

(0, 1), (0, - 1), (1, 0), (- 1, 0)

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 1), (0, - 1), (1, 0), (- 1, 0)

f (x) = 3 x^{2} + 4 x + 1

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

5 + 6 x^{2} - x^{4}

f (x) = 3 x^{2} + 4 x - 4

f (x) = 3 x^{2} - 8 x + 4

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