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)

f (x) = x^{3} + 8

f (x) = \frac{900}{x} + 2 π x^{2}

\frac{ln ( x )}{x ^{3}}

f (x) = - (25 - x^{2})^{2}

f (x) = (x - 3)^{\frac{4}{3}}

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)