Coming up with a counter example - calculus

I have to come up with a counter example for the following statement:

Let $f$ be a function $f: [0,\infty)\longrightarrow R$, continuous and bounded. Prove that it receives either a minimum or a maximum (or both)

Everything I tried seems to always be lacking one of the conditions, for example $\sin(1/x)$ is not continuous at $0$, $x\sin(x)$ is bounded, $\sin(x) + 1/x$ does have a minimum

Any help would be appreciated.