What is the critical f(x,y)=x^3-2xy+y^2+4 ?

The critical f(x,y)=x^3-2xy+y^2+4 is (2/3 , 2/3),(0,0)

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critical f(x,y)=x^3-2xy+y^2+4

critical points

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

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

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

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

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

f (x) = x^{3} - 9 x^{2} + 24 x - 10

f (x, y) = x y + 5 x - 5

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

f (x) = \frac{1}{4} x^{4} - 2 x^{2}

What is the critical f(x,y)=x^3-2xy+y^2+4 ?
The critical f(x,y)=x^3-2xy+y^2+4 is (2/3 , 2/3),(0,0)