Question

infinity times infinity is infinity

Answer 1

not on the open interval, no

Answer 2

think of a simple function, the identity \(f(x)=x\) on \((a,b)\)

Answer 3

it attains neither a max nor a min, since the min would be \(a\) but \(a\) is not in that interval
ditto for max

Answer 4

Okay thank you so basically in some cases f(x) will not have a maximum value?