$f(x)=[x]$ for $x\in [5,9]$
In the interval $[5,9],f(x)=[x]$ is neither continuous nor derivable at $x=6,7,8$.Hence Rolle's theorem is not applicable.
$f(x)=[x]$ is the greatest integer less than or equal to $x$
$f'(x)=0$.But f is neither continuous nor differentiable in the interval $[5,9]$