What is the extreme f(x,y)=x^2+y^2+12x-16y ?

The extreme f(x,y)=x^2+y^2+12x-16y is Minimum(-6,8)

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extreme f(x,y)=x^2+y^2+12x-16y

extreme

Minimum (- 6, 8)

Solution steps

Find the critical points:

(- 6, 8)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(- 6, 8) :

Minimum

Minimum (- 6, 8)

What is the extreme f(x,y)=x^2+y^2+12x-16y ?
The extreme f(x,y)=x^2+y^2+12x-16y is Minimum(-6,8)