A continuous real function on an interval takes every value between its endpoint values.Suggest a slogan
Let \(a<b\) and let \(f\colon[a,b]\to\RR\) be continuous with \(f(a)<f(b)\). For every \(y\in\RR\) with \(f(a)<y<f(b)\) there exists \(c\in(a,b)\) such that \(f(c)=y\). [@Rud76].