What is the extreme f(x,y)=4xy-x^2-y^2-14x+4y+10 ?

The extreme f(x,y)=4xy-x^2-y^2-14x+4y+10 is Saddle(1,4)

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extreme f(x,y)=4xy-x^2-y^2-14x+4y+10

extreme points

f (x, y) = 4 x y - x^{2} - y^{2} - 14 x + 4 y + 10

Saddle (1, 4)

Solution steps

Find the critical points:

(1, 4)

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

D (x, y) = - 12

Check the sign of at each critical point

Check critical point

(1, 4) :

Saddle

Saddle (1, 4)

What is the extreme f(x,y)=4xy-x^2-y^2-14x+4y+10 ?
The extreme f(x,y)=4xy-x^2-y^2-14x+4y+10 is Saddle(1,4)