Intermediate value theorem

The intermediate value theorem says that if a function, , is continuous over a closed interval , and is equal to  and  at either end of the interval, for any number, c, between  and , we can find an  so that . 

This means that if a continuous function's sign changes in an interval, we can find a root of the function in that interval. For example, if  and , we can find an  in the interval  that is a root of this function, meaning that for this value of x, , if  is continuous. This corollary is called Bolzano's theorem.

 References  

Category:Mathematical theorems
Category:Mathematical analysis