My original approach was to let $f = \sin (1/x)$ and do regular calculus. However, I found that it wasn't so simple. I graphed the function on Mathematica and it was even worse!
It seems like the function tends to infniity near the origin (or negative infinity?) IN either case, I don't think it is bounded above nor does a supermum exist because of the singularity.
Any insights?
inf is -1/pi, sup does not exist