What is the extreme f(x,y)=2x^2-8y^2-4x+9y+2 ?

The extreme f(x,y)=2x^2-8y^2-4x+9y+2 is Saddle(1, 9/16)

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extreme f(x,y)=2x^2-8y^2-4x+9y+2

extreme

Saddle (1, \frac{9}{16})

Solution steps

Find the critical points:

(1, \frac{9}{16})

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

D (x, y) = - 64

Check the sign of at each critical point

Check critical point

(1, \frac{9}{16}) :

Saddle

Saddle (1, \frac{9}{16})

What is the extreme f(x,y)=2x^2-8y^2-4x+9y+2 ?
The extreme f(x,y)=2x^2-8y^2-4x+9y+2 is Saddle(1, 9/16)