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

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

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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)

ln (x) - 3 x + 2

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

f (x, y) = 5 - (x - 3)^{2} - (y + 2)^{2}

- 3 x^{2} + 5 x y - 2 y^{2} + x + y

f (x) = - x^{2} + 6 x + 1, 5 \leq x \leq 8

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