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

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

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

critical points

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

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

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

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

f (x, y) = - x^{4} - 32 x + y^{3} - 12 y + 7

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

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

\frac{3 x}{x ^{2} - 16}

4 x^{3} - 16 x

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