Consider : $f(x) = 2^{\lfloor x \rfloor - x}$ . We want to find minimum of $f(x)$. I know that $f(x)$ is not continuous and periodic function but what we can say about minimum and maximum of it ? (Its minimum or maximum is global or local ?)
Please Help!
Clearly, a periodic function cannot have a strict global maximum, since every value on $[0,1)$ repeats on $[1,2)$.
However, you can easily find maximums of $f$ on $[0,1)$ and each maximum on this interval will be one of an infinite family of maximums. Same for minumums.