What is the extreme f(x,y)=x^2+y^2-2x-6y+14 ?

The extreme f(x,y)=x^2+y^2-2x-6y+14 is Minimum(1,3)

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extreme f(x,y)=x^2+y^2-2x-6y+14

extreme points

f (x, y) = x^{2} + y^{2} - 2 x - 6 y + 14

Minimum (1, 3)

Solution steps

Find the critical points:

(1, 3)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(1, 3) :

Minimum

Minimum (1, 3)

What is the extreme f(x,y)=x^2+y^2-2x-6y+14 ?
The extreme f(x,y)=x^2+y^2-2x-6y+14 is Minimum(1,3)