What is the critical x^3-2xy+y^2+4 ?

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

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critical x^3-2xy+y^2+4

critical points

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^{2} + 2 x y + 2 y^{2} - 6 x + 10 y + 6

\frac{8 x ^{2} - 24 x}{3 ( x + 1 ) ^{\frac{1}{3}}}

f (x) = 6 x^{2} + 2 x - 12

8 - (x + 3)^{2}

x^{2} - 16

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