Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics II / 6 / a / i / Solution

The mean value theorem states that if $f:[a,b]\to \mathbb{R}$ is continuous on $[a,b]$ and differentiable on $(a,b)$, where $a<b$, there is $c\in (a,b)$ such thatNo continuity assumption on the derivative is needed.