What is the extreme f(x,y)=(x-0.5)^2-y^2 ?

The extreme f(x,y)=(x-0.5)^2-y^2 is Saddle(0.5,0)

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extreme f(x,y)=(x-0.5)^2-y^2

extreme points

f (x, y) = (x - 0.5)^{2} - y^{2}

Saddle (0.5, 0)

Solution steps

Find the critical points:

(0.5, 0)

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

D (x, y) = - 4

Check the sign of at each critical point

Check critical point

(0.5, 0) :

Saddle

Saddle (0.5, 0)

f (x) = - \frac{15}{x ^{2} + 3}

x^{2} - 5 x + 8

f (y, x) y = \frac{x ^{3}}{3} - x^{2} - 24 x - 8

f (x) = \frac{16 x ^{2} + 25}{x}

y = 9 - x

What is the extreme f(x,y)=(x-0.5)^2-y^2 ?
The extreme f(x,y)=(x-0.5)^2-y^2 is Saddle(0.5,0)