An example of a continuous function such that $M$ is the maximum of $f$ on $[a,b]$, and that $\{x\_i\}$ is a sequence on $[a,b]$ such that $f(x\_i)$ converges to $M$ but $\{x\_i\}$ is not convergent. I'm confused as to how I can find such a function and what sequence I should be looking for.