# Its an entrance exam problem based on Calculus

• Feb 16th 2013, 04:36 AM
tejasnatu
Its an entrance exam problem based on Calculus
Let f : R -> R be a continuous function such that f(x + 1) = f(x), for all x. Then f
attains its supremum. Is this statement true or false?? Give reasons...???
• Feb 16th 2013, 07:15 AM
emakarov
Re: Its an entrance exam problem based on Calculus
Well, f attains its supremum on [0,1]...
• Feb 16th 2013, 08:31 AM
tejasnatu
Re: Its an entrance exam problem based on Calculus
See the extreme value theorem. And the values of f on $\mathbb{R}\setminus[0,1]$ are the same as on [0, 1].