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

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

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

extreme points

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

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

Solution steps

Find the critical points:

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

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

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

Minimum

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

f (x) = 2 x^{3} + 9 x^{2} - 24 x - 10

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

f (x) = x^{2} + 3 x - 9

f (x) = \frac{25 x ^{2} + 81}{x}

K (y, z) = 4 yz

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