Intermediate value theorem

In mathematical analysis, the intermediate value theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval. This has two important corollaries: 1. * If a continuous function has values of opposite sign inside an interval, then it has a root in that interval (Bolzano's theorem). 2. * The image of a continuous function over an interval is itself an interval.

Intermediate value theorem

In mathematical analysis, the intermediate value theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval. This has two important corollaries: 1. * If a continuous function has values of opposite sign inside an interval, then it has a root in that interval (Bolzano's theorem). 2. * The image of a continuous function over an interval is itself an interval.