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) = x^{3} + 9

f (x) = \frac{x ^{2} - 7}{x + 4}

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

f (x) = 4 x - x

f (x) = x^{3} - 9 x^{2} + 6

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)