I'm having trouble finding out how to tell if a critical point is within a region

for example If I want to find the maximum value of $$f(x,y)=x^2+y^2-2x$$in the plane region R, where R is a triangle with vertices at (0,0) (2,0) and (0,2).

So I know that the only critical point on this curve is at (1,0) and I also can see that it's not the maximum anyways, but it actually could be the miniumum of the region as long as I know that it is in the region! so how would I tell if it is?

Question

I'm having trouble finding out how to tell if a critical point is within a region

for example If I want to find the maximum value of $$f(x,y)=x^2+y^2-2x$$in the plane region R, where R is a triangle with vertices at (0,0) (2,0) and (0,2).

So I know that the only critical point on this curve is at (1,0) and I also can see that it's not the maximum anyways, but it actually could be the miniumum of the region as long as I know that it is in the region! so how would I tell if it is?