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

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

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

extreme points

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

Minimum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Minimum (0, 0)

f (x, y) = x^{3} + y^{2} - 6 x^{2} + y - 1

f (x) = x^{2} - 5 x + 1

f (x, y) = e^{4 x y} + 5 y

f (x) = \frac{x}{2} - cos (x)

f (x) = - 2 (4 x - 5) e^{4 x}

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