The intermediate value theorem states that if a function is continuous on [ a , b ] {\displaystyle \displaystyle [a,b]} and f ( a ) < 0 < f ( b ) {\displaystyle \displaystyle f(a)<0<f(b)} or f ( b ) < 0 < f ( a ) {\displaystyle \displaystyle f(b)<0<f(a)} , then there exists a point c ∈ ( a , b ) {\displaystyle \displaystyle c\in (a,b)} such that f ( c ) = 0 {\displaystyle \displaystyle f(c)=0} .
![{\displaystyle \displaystyle [a,b]}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/f88200110d0856db1980407567cafff36cef1e5d)
