I am trying to prove this inequality but I don't seem to have any lead. Any suggestions?
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
Hint: If you can prove that $f(x)\cdot g(x) \leq \sup(f)\cdot \sup(g)$, for all $x$, what you want will follow because you will have proven that $\sup(f)\cdot \sup(g)$ is an upper bound of $f\cdot g$ and therefore it's greater than the smallest upper bound.