Mój problem jest następujący:My problem is as follows

Let $\displaystyle f(x)=xh(x)$, where $\displaystyle h(x)$ is periodic function with period 1. Prove or give a counterexample to the following statement: Function $\displaystyle f$ is increasing if and only if $\displaystyle h$ is constant (and the constant is positive). We assume that $\displaystyle h$ is defined on the whole R.

Thank you for help