Finding extrema on open or unbounded intervals is similar to the process for closed intervals. For instance, say you want to optimize a function f over the reals (which form an unbounded interval, namely (−∞,∞)). If, say, f(x)≤f(a) for all x≤a and f(x)≤f(b) for all x≥b (e.g. imagine f increasing up to a and decreasing after b), then to find the global maxima of f on the interval R=(−∞,∞), you can restrict your attention to the closed interval [a,b], which we already know how to analyze.
