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

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

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

extreme points

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

Minimum (- 1, 0)

Solution steps

Find the critical points:

(- 1, 0)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(- 1, 0) :

Minimum

Minimum (- 1, 0)

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