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

The extreme f(x,y)=x^2+xy+y^2-4x-2y is Minimum(2,0)

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

extreme points

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

Minimum (2, 0)

Solution steps

Find the critical points:

(2, 0)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(2, 0) :

Minimum

Minimum (2, 0)

f (x) = 4 x + 9 x^{- 1}

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

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

f (x, y) = x^{2} y - 5 x y^{3}

\frac{x + 4}{x - 3}

What is the extreme f(x,y)=x^2+xy+y^2-4x-2y ?
The extreme f(x,y)=x^2+xy+y^2-4x-2y is Minimum(2,0)