Loterre: Mathématiques: extreme value theorem

mathematical analysis > real analysis > extreme value theorem

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extreme value theorem

In calculus, the extreme value theorem states that if a real-valued function ${\\displaystyle f}$ is continuous on the closed interval ${\\displaystyle [a,b]}$ , then ${\\displaystyle f}$ must attain a maximum and a minimum, each at least once. That is, there exist numbers ${\\displaystyle c}$ and ${\\displaystyle d}$ in ${\\displaystyle [a,b]}$ such that: ${\\displaystyle f(c)\\geq f(x)\\geq f(d)\\quad \ orall x\\in [a,b]}$
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Extreme_value_theorem)

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