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

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

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

extreme points

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

Minimum (0, 1)

Solution steps

Find the critical points:

(0, 1)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(0, 1) :

Minimum

Minimum (0, 1)

f (x) = x^{2} - 12 x + 5

f (x) = x^{2} - y^{2} + 21

f (x, y) = (9 x^{2} + 4 x + 5) (9 y^{2} + 6 y + 6)

f (x) = 6 x^{3} - x^{2} - 5 x + 7

f (x) = γ (x + 1)

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