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在开区间或无界区间求极值

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减少到闭区间的情况

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 $(-\infty,\infty)$ ). If, say, $f(x) \le f(a)$ for all $x\le a$ and $f(x)\le f(b)$ for all $x\ge b$ (e.g. imagine $f$ increasing up to $a$ and decreasing after $b$ ), then to find the global maxima of $f$ on the interval $\mathbb{R} = (-\infty,\infty)$ , you can restrict your attention to the closed interval $[a,b]$ , which we already know how to analyze.

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