↑ stuart clark:
Dear stuart, here are some hints...
One can easily see that the given function is
-periodic. If we further denote
then by considering the intervals
we deduce immediately that f_1 is increasing on I_1 and decreasing on I_2. Exactly the same holds for the function f_2. (It suffices to take into acount the monotonicity of all parts of the composite function f_1 and their ranges related to the intervals I_1, I_2; analogical for f_2). Due to these properties, the function f=f_1+f_2 has exactly the same monotonicity behaviour.
Finally, this enables to say that the minimal values occur for
and the maximal values occur for