Answer
See explanations.
Work Step by Step
Step 1. If a function has no endpoints, this means that its domain should be $(-\infty, \infty)$
Step 2. If a function $f$ has no critical points, this means that it is differentiable in the domain and $f'(x)\ne0$.
Step 3. We can find examples that $f'(x)=constant\ne0$, such as $f(x)=2x$ which satisfy the conditions. In this case, there will not be any extrema for the function.