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

The extreme f(x,y)=x^2-y^2+x+y+5 is Saddle(-1/2 , 1/2)

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

extreme points

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

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

Solution steps

Find the critical points:

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

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

D (x, y) = - 4

Check the sign of at each critical point

Check critical point

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

Saddle

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

f (x) = - x^{2} - x + 1

f (x, y) = 5 x^{2} + 3 x y + 10 y^{2} + 4 x y^{2} + 6 x^{2} y

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

f (x) = 3 x^{3} + 3 x^{2} - 10 x - 2

f (x) = 0.0001 x^{2} + 3.2 x - 90

What is the extreme f(x,y)=x^2-y^2+x+y+5 ?
The extreme f(x,y)=x^2-y^2+x+y+5 is Saddle(-1/2 , 1/2)