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

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

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

extreme points

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

Saddle (\frac{9}{2}, - 1)

Solution steps

Find the critical points:

(\frac{9}{2}, - 1)

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

D (x, y) = - 4

Check the sign of at each critical point

Check critical point

(\frac{9}{2}, - 1) :

Saddle

Saddle (\frac{9}{2}, - 1)

f (x) = 2 x^{3} - 9 x^{2} + 3, - 2 \leq x \leq 2

f (x, y) = x^{3} + y^{3} + 3 x y^{2} - 18 x - 18 y

f (x) = 2 x^{4} - 36 x^{2}

f (x) = 25 (x^{2} - y^{2}) - 2 (x^{2} + y^{2})^{2}

f (x) = 2 x^{3} + 4 x^{2} + 2 x

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