What is Intermediate value theorem?
The '''intermediate value theorem''' says that if a function, <math>f</math>, is [[continuous function|continuous]] over a [[Interval (mathematics)|closed interval]] <math>[a,b]</math>, and is equal to <math>f(a)</math> and <math>f(b)</math> at either end of the interval, for any number, c, between <math>f(a)</math> and <math>f(b)</math>, we can find an <math>x</math> so that <math>f(x) = c</math>. This means that if a continuous function's sign changes in an interval, we can find a [[root of a function|root]] of the function in that interval. For example, if <math>f(1) = -1</math> and <math>f(2) = 2</math>, we can find an <math>x</math> in the interval <math>[1,2]</math> that is a '''root''' of this function, meaning that for this value of x, <math>f(x)=0</math>, if <math>f</math> is continuous. This [[corollary]] is called '''Bolzano's theorem'''.<ref>{{cite web|last=Weisstein|first=Eric|title=Bolzano's Theorem|url=http://mathworld.wolfram.com/BolzanosTheorem.html|publisher=[[Wolfram Research]]|access-date=26 November 2017}}</ref> == References == {{reflist}} {{math-stub}} [[Category:Mathematical theorems]] [[Category:Mathematical analysis]]