Past exam of the mathematics course of the University of Cambridge / 2013 / ia / Paper 1 / 10E / b / Solution

The intermediate value theorem states that a real-valued continuous function on a closed interval takes every value between its endpoint values. Explicitly, if $v$ lies between $f(s)$ and $f(t)$, there exists $u\in [s,t]$ with $f(u)=v$. No monotonicity is assumed.