Extreme Value Theorem: If $f$ is a continuous function on an interval [a,b], then $f$ attains its maximum and minimum values on [a,b]. Proof from my book: Since $f ...

Jul 28, 2018 · The extreme value theorem proves the existence of global maxima and minima for a continuous function in a closed interval.This theorem is actually, pretty much intuitive and …

Jul 27, 2018 · The extreme value theorem requires a closed interval. The max / min may be at an endpoint. Over an open interval there may not be a max or a min. Rolles theorem / MVT still …

Jul 29, 2014 · I think that there is a more general version of the extreme value theorem which states a similar result for a closed and bounded subset of $\mathbb {R}^n$. (At least I think I …

May 16, 2015 · Theorem: In calculus, the extreme value theorem states that if a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain a maximum …

Oct 2, 2017 · I have reached section 3.1 in Stewart's Calculus book. I see the Extreme Value theorem. (The theorem says that a continuous function defined on a closed interval attains …

Soo.. Do you want a prove for the Intermediate Value Thm without (sub-)sequences, or you want to deduce the Extreme Value Thm using the Interm.Value thm, by halfing the interval in …

Nov 19, 2025 · The simple reason the extreme value theorem is used is because it is necessary. Suppose you are in a situation where the extreme value theorem does not apply, say …

Each of the following statement follows from either the Intermediate Value Theorem, the Extreme Value Theorem, or the Mean Value Theorem. Determine which one in each case.

Feb 6, 2019 · The extreme value theorem is just about continuity - it says that continuous functions achieve maximal and minimal values on (finite) closed intervals (in their domains).