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

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

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extreme f(x,y)=(x-1)^2-(y-1)^2

extreme points

f (x, y) = (x - 1)^{2} - (y - 1)^{2}

Saddle (1, 1)

Solution steps

Find the critical points:

(1, 1)

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

D (x, y) = - 4

Check the sign of at each critical point

Check critical point

(1, 1) :

Saddle

Saddle (1, 1)

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

f (x) = 161000 x - 100 x^{21}

f (x) = - 6 x^{2} e^{- x} - 4

f (x) = 2.2 + 2.6 x - 0.8 x^{2}

f (x) = - 4 x^{3} + 12 x^{2} + 36 + 3

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