The Definition of absolute max and min is attached. My question is in an interval I=[0,2] and f(x) = x, if 0<=x<1 and x-2 if 1<=x<=2 Why is it does not have a aboslute max?
I understand that this is trying to show that if a function is dis-continous the theorem is failes. but I think the there still exist an absolute max and that is y=0.
Since here we are only looking at the max or min value which in the definition it just says that there exist a point a in S that f(x) <= f(a) for all x in S. In this case, this is ture for all x such that f(x) <= f(a) = 0; so it is valid to say that at point x=2, it's the absolute max since very other x has a f(x) that < or = f(2).
Thanks.
I understand that this is trying to show that if a function is dis-continous the theorem is failes. but I think the there still exist an absolute max and that is y=0.
Since here we are only looking at the max or min value which in the definition it just says that there exist a point a in S that f(x) <= f(a) for all x in S. In this case, this is ture for all x such that f(x) <= f(a) = 0; so it is valid to say that at point x=2, it's the absolute max since very other x has a f(x) that < or = f(2).
Thanks.
