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

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

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

extreme points

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

Saddle (1, 1)

Solution steps

Find the critical points:

(1, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 4

Check the sign of at each critical point

Check critical point

(1, 1) :

Saddle

Saddle (1, 1)

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