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

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

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

critical points

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

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

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

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

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

2 x^{2} - x^{4}

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

x^{4} - 8 x^{2} + 16

y = 3 x^{3} - 2 x^{2} - 5 x

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