What is the extreme f(x,y)=x^2-xy+y^2+9x-6y+10 ?

The extreme f(x,y)=x^2-xy+y^2+9x-6y+10 is Minimum(-4,1)

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extreme f(x,y)=x^2-xy+y^2+9x-6y+10

extreme points

f (x, y) = x^{2} - x y + y^{2} + 9 x - 6 y + 10

Minimum (- 4, 1)

Solution steps

Find the critical points:

(- 4, 1)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(- 4, 1) :

Minimum

Minimum (- 4, 1)

What is the extreme f(x,y)=x^2-xy+y^2+9x-6y+10 ?
The extreme f(x,y)=x^2-xy+y^2+9x-6y+10 is Minimum(-4,1)