Answer
See graph and explanations.
Work Step by Step
A function $f(x)$ has no endpoints on an open interval $(a,b)$. However, it may have at least one local (or absolute) extreme as shown in the figure, where the function has both a local/absolute maximum and a minimum. For a half open interval such as $[a,b)$, the function will have one endpoint and thus at least one local extreme.
