将开区间的端点代入计算

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 $(0,\infty)$ , and you know that $\lim_{x\to0^+} f(x) = 57$ , while $\lim_{x\to\infty} f(x) = 2017$ . Then $f$ is minimized at some critical point $c\in (0,\infty)$ if $f(c) < 57$ , but it's possible that $f(c) > 57$ for every critical point $c\in (0,\infty)$ , in which case $f$ is not minimized at an actual point of $(0,\infty)$ , but rather "minimized as $x$ approaches $0$ from the right".

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将开区间的端点代入计算

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