Let $[a, b] \subseteq \mathbb{R}$ be a D544: Closed real interval such that

(i)	\begin{equation} a < b \end{equation}
(ii)	$f : [a, b] \to \mathbb{R}$ is a D5231: Standard-continuous real function on $[a, b]$
(iii)	$f$ is a D5614: Differentiable real function on $(a, b)$
(iv)	\begin{equation} f(a) = f(b) \end{equation}

Then \begin{equation} \exists \, x \in (a, b) : f'(x) = 0 \end{equation}