What is the extreme f(x,y)=5x^2-4xy+y^2-16x-12y-4 ?

The extreme f(x,y)=5x^2-4xy+y^2-16x-12y-4 is Minimum(20,46)

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extreme f(x,y)=5x^2-4xy+y^2-16x-12y-4

extreme points

f (x, y) = 5 x^{2} - 4 x y + y^{2} - 16 x - 12 y - 4

Minimum (20, 46)

Solution steps

Find the critical points:

(20, 46)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(20, 46) :

Minimum

Minimum (20, 46)

What is the extreme f(x,y)=5x^2-4xy+y^2-16x-12y-4 ?
The extreme f(x,y)=5x^2-4xy+y^2-16x-12y-4 is Minimum(20,46)