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

The extreme f(x,y)=x^2+y^2-xy-2x+y is Minimum(1,0)

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

extreme points

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

Minimum (1, 0)

Solution steps

Find the critical points:

(1, 0)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(1, 0) :

Minimum

Minimum (1, 0)

f (x) = - x^{3} - 12 x^{2}

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

f (x) = 90 x^{2} - 0.2 x^{4}

f (x \cdot y) = 3 x^{2} - 4 x y + 3 y^{2} + 8 x - 17 y + 5

x^{3} - 16 x y + 4 y^{2} + 16 x^{2} - 12 x + 5

What is the extreme f(x,y)=x^2+y^2-xy-2x+y ?
The extreme f(x,y)=x^2+y^2-xy-2x+y is Minimum(1,0)