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

The extreme f(x,y)=x^2+xy-y^2-y is Saddle(1/5 ,-2/5)

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

extreme points

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

Saddle (\frac{1}{5}, - \frac{2}{5})

Solution steps

Find the critical points:

(\frac{1}{5}, - \frac{2}{5})

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

D (x, y) = - 5

Check the sign of at each critical point

Check critical point

(\frac{1}{5}, - \frac{2}{5}) :

Saddle

Saddle (\frac{1}{5}, - \frac{2}{5})

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

f (x) = 3 x^{2} + \frac{48}{x ^{2}}

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

f (x) = 2 x y - 15 y^{2}

f (x) = 6 sin (x) + cot (x)

What is the extreme f(x,y)=x^2+xy-y^2-y ?
The extreme f(x,y)=x^2+xy-y^2-y is Saddle(1/5 ,-2/5)