Ivan Shishkin, Birch Grove

Intermediate value theorem

Concept history

A revision trail for this concept page.

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Revision 3809

9/4/2026, 3:17:02 PM · T.W

Added exercise "Application du TVI à une équation fonctionnelle."

linked exercisesExistence d’une solution pour une équation de degré 2Existence d’une racine carrée, Application du TVI à une équation fonctionnelle.

Revision 3576

9/2/2026, 1:37:56 PM · Ancient Tree

Added exercise "Existence d'une solution pour une équation de degré 2"

linked exercisesNoneExistence d’une solution pour une équation de degré 2

Revision 1073

8/8/2026, 8:57:11 AM · Ancient Tree

Concept created

##### Intuition
A continuous function cannot move from one value to another without taking every intermediate value along the way.
For example, if you are hiking, and your altitude (a continuous function of time) starts at $1000$ and ends at $2000$, then you can be sure that at some point during the hike, the altitude will be exactly $1257$.

##### Statement
Let $f:[a,b]\rightarrow \R$ be a [[continuous function|continuous function]] on the [[Closed interval|closed interval]] $[a,b]$. If $L$ is any real number between $f(a)$ and $f(b)$, then there exists at least one $c$ in $[a,b]$ such that
$$f(c)=L.$$
.