What is the extreme f(x)=x^2+y^2+18x-6y ?

The extreme f(x)=x^2+y^2+18x-6y is Minimum(-9,3)

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extreme f(x)=x^2+y^2+18x-6y

extreme points

f (x) = x^{2} + y^{2} + 18 x - 6 y

Minimum (- 9, 3)

Solution steps

Find the critical points:

(- 9, 3)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(- 9, 3) :

Minimum

Minimum (- 9, 3)

What is the extreme f(x)=x^2+y^2+18x-6y ?
The extreme f(x)=x^2+y^2+18x-6y is Minimum(-9,3)