Is the following statement true?
If $f(x) \geq 0$ for all $x$, and $\displaystyle{}\int_{-\infty}^{\infty} f(x) d x<\infty$ then $\displaystyle{}\int_{-\infty}^{\infty} x^{2} f(x) d x \geq \epsilon^{2} \int_{\epsilon}^{\infty} f(x) d x$, for all $\epsilon>0$.
