What is the extreme f(x,y)=3x^2+4xy-4y^2-x+3y ?

The extreme f(x,y)=3x^2+4xy-4y^2-x+3y is Saddle(-1/16 , 11/32)

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extreme f(x,y)=3x^2+4xy-4y^2-x+3y

extreme

Saddle (- \frac{1}{16}, \frac{11}{32})

Solution steps

Find the critical points:

(- \frac{1}{16}, \frac{11}{32})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 8

D (x, y) = - 64

Check the sign of at each critical point

Check critical point

(- \frac{1}{16}, \frac{11}{32}) :

Saddle

Saddle (- \frac{1}{16}, \frac{11}{32})

What is the extreme f(x,y)=3x^2+4xy-4y^2-x+3y ?
The extreme f(x,y)=3x^2+4xy-4y^2-x+3y is Saddle(-1/16 , 11/32)