Finding extrema on open or unbounded intervals is similar to the process for closed intervals. However, when finding global extrema, you might need to be a little more careful with "boundary" analysis: what happens in the limit as you approach endpoints (for open intervals) or infinity (for unbounded intervals). For example, suppose you are trying to minimize a differentiable function f over the unbounded interval (0,∞), and you know that limx→0+f(x)=57, while limx→∞f(x)=2017. Then f is minimized at some critical point c∈(0,∞) if f(c)<57, but it's possible that f(c)>57 for every critical point c∈(0,∞), in which case f is not minimized at an actual point of (0,∞), but rather "minimized as x approaches 0 from the right".
