\begin{frame} \frametitle{Mean Value Theorem} \meanvalueshort \begin{exampleblock}{} Let $s(t)$ be the position of an object after time $t$. \pause\medskip Then the average velocity between time $t = a$ and $t = b$ is: \begin{talign} \frac{s(b) - s(a)}{b-a} \end{talign} \pause What does the Mean Value Theorem tell us? \pause\medskip It states that there is a time $c$ between $a$ and $b$ such that \begin{talign} f'(c) = \frac{s(b) - s(a)}{b-a} \quad \text{, \quad that is} \end{talign} the instantaneous velocity at $c$ is equal to the average velocity. \end{exampleblock} \vspace{10cm} \end{frame}