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

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

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

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 5

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = - x^{2} + 4 x + 5

f (x, y) = \frac{( 2 x + y )}{3}

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

f (x) = x^{2} + x y + \frac{1}{2} y^{2} - 4 x + y

f (x) = \frac{1}{3} x^{3} - 2 x^{2} - 5 x + 2

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