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

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

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

extreme points

f (x) = y^{2} - x^{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) = \frac{1}{x - 2} - 3

T (x, y) = (x + 3 y, - x + 5 y)

f (x) = x (12 - 2 x)^{2}

f (x, y) = 8 x^{3} + y^{3} + 6 x y

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