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

The extreme f(x)=x^2+y^2-xy+x+y is Minimum(-1,-1)

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extreme f(x)=x^2+y^2-xy+x+y

extreme points

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

Minimum (- 1, - 1)

Solution steps

Find the critical points:

(- 1, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(- 1, - 1) :

Minimum

Minimum (- 1, - 1)

f (x) = \frac{x}{1 - x}

f (x) = 2 x + 4 y

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

f (x) = x e^{- 7 x^{2}}

f (x) = \frac{1}{3} x^{3} - \frac{1}{3} x^{2} - 2 x

What is the extreme f(x)=x^2+y^2-xy+x+y ?
The extreme f(x)=x^2+y^2-xy+x+y is Minimum(-1,-1)