What is the extreme f(x,y)=7x^2-9y^2+2x+9y+6 ?

The extreme f(x,y)=7x^2-9y^2+2x+9y+6 is Saddle(-1/7 , 1/2)

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extreme f(x,y)=7x^2-9y^2+2x+9y+6

extreme points

f (x, y) = 7 x^{2} - 9 y^{2} + 2 x + 9 y + 6

Saddle (- \frac{1}{7}, \frac{1}{2})

Solution steps

Find the critical points:

(- \frac{1}{7}, \frac{1}{2})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 18

D (x, y) = - 252

Check the sign of at each critical point

Check critical point

(- \frac{1}{7}, \frac{1}{2}) :

Saddle

Saddle (- \frac{1}{7}, \frac{1}{2})

U (x, t) = e^{(x^{2} - t^{2})}

f (x, y) = - 6 x^{2} + 4 y^{2} + 2 x + 4 y + 8

f (x, y) = \frac{x ^{2}}{2} - \frac{y ^{2}}{2}

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

P (x, y) = 6 x^{2} + 19 x y + 15 y^{2} - 17 y - 11 x + 4

What is the extreme f(x,y)=7x^2-9y^2+2x+9y+6 ?
The extreme f(x,y)=7x^2-9y^2+2x+9y+6 is Saddle(-1/7 , 1/2)