What is the extreme f(x,y)=8y^2-5x^2-10y+2xy ?

The extreme f(x,y)=8y^2-5x^2-10y+2xy is Saddle(5/41 , 25/41)

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extreme f(x,y)=8y^2-5x^2-10y+2xy

extreme points

f (x, y) = 8 y^{2} - 5 x^{2} - 10 y + 2 x y

Saddle (\frac{5}{41}, \frac{25}{41})

Solution steps

Find the critical points:

(\frac{5}{41}, \frac{25}{41})

\frac{\partial ^{2} f}{\partial x ^{2}} = 16

D (x, y) = - 164

Check the sign of at each critical point

Check critical point

(\frac{5}{41}, \frac{25}{41}) :

Saddle

Saddle (\frac{5}{41}, \frac{25}{41})

What is the extreme f(x,y)=8y^2-5x^2-10y+2xy ?
The extreme f(x,y)=8y^2-5x^2-10y+2xy is Saddle(5/41 , 25/41)