
with floor functions
Show that the function:
$\displaystyle f(x) = \frac{x  \lfloor x \rfloor}{x + \lfloor x \rfloor +1}$ is:
a) always uppersemicontinuous;
b) has a derivative for all x belonging to N (natural numbers).
Thanks in advance for the help all you mathwizzes out there.

sorry folks I made a terrible typing mistake.
the question's part b should be:
b) for all x not belonging to Z.
And now that I come to think of it the solution is rather simple, so I take back the question to this part.
However part a) is still puzzling me (and I'm sure there are no typos here) Any ideas?