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

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

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

critical points

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

(- \frac{2}{3}, - \frac{4}{3})

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

(- \frac{2}{3}, - \frac{4}{3})

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

f (x, y) = x y + \frac{216}{x} + \frac{216}{y}

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

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

f (x) = 4 x y - x^{4} - y^{4}

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