Answer
The function could either be always increasing or always decreasing. For instance, on the domain $[a,b]$, if $f$ is always decreasing (i.e. $f(x) = -x$), then the $\textbf{absolute minimum}$ value would be at point $b$.
Work Step by Step
The explanation given is one way that a function can have its $\textbf{absolute minimum}$ at the endpoint of an interval.
