What is the extreme f(x,y)=100+x^2-y^2 ?

The extreme f(x,y)=100+x^2-y^2 is Saddle(0,0)

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extreme f(x,y)=100+x^2-y^2

extreme points

f (x, y) = 100 + x^{2} - y^{2}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 4

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

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

f (x) = - 2 x^{4} + 16 x^{3} - 26

f (x) = (x - 5)^{2} + 3

f (x, y) = 1 - x + y

f (x, y) = x^{2} y - 2 x y^{2} + 8 y^{3}

What is the extreme f(x,y)=100+x^2-y^2 ?
The extreme f(x,y)=100+x^2-y^2 is Saddle(0,0)