![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/8/83/Illustration_for_the_intermediate_value_theorem.svg/640px-Illustration_for_the_intermediate_value_theorem.svg.png&w=640&q=50)
Intermediate value theorem
Continuous function on an interval takes on every value between its values at the ends / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Bolzano's theorem?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In mathematical analysis, the intermediate value theorem states that if is a continuous function whose domain contains the interval [a, b], then it takes on any given value between
and
at some point within the interval.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/8/83/Illustration_for_the_intermediate_value_theorem.svg/320px-Illustration_for_the_intermediate_value_theorem.svg.png)
This has two important corollaries: