[Lecture 13] Mean Value Theorem

Suppose that \(a,b \in \mathbb{R}\) with \(a < b\). If

1. \(f\) is continuous on \([a,b]\)
2. \(f\) is differentiable on \((a,b)\)

Then $$ \begin{align*} f'(c) = \frac{f(b) - f(a)}{b - a} \end{align*} $$