I have this function :
$f(x,y)=x²+y²-2y-x$
I want to find the absolute min/max of the function on the set given in the figure below (where L3 is a piece of a circle with center (0, 0).
I've already describes lines 1 and 2 and found their critical points. Now working with L3 i see on the answer sheet that it is described as
$L3=((x,y): x²+y²=3², −3 ≤ x ≤ 0)$
May I ask you where they are getting the 3² ? I know it may be a dumb question but i just recently started studying the concept of absolute min and max, moreover with coordinates that make it quite harder. Thanks!
The formula of the circle at origin with radius $r$ is $x^2+y^2=r^2$, here the radius is $3$.
As for the origin problem, you might like to visualize $f$ as
$$x^2+y^2-2y-x=(x-\frac12)^2-\frac14+(y-1)^2-1$$