Let $\mathbb{R}$ denote the \reftext{def:real-numbers-c54-2026c}{real numbers} and let $f:\mathbb{R}\to\mathbb{R}$ be a \reftext{def:ck-map-euclidean-open-set-2026b}{$C^3$ map} on $\mathbb{R}=\mathbb{R}^1$, and suppose its third derivative is bounded: there is $M_3\ge 0$ with $|f'''(x)|\le M_3$ for all $x\in\mathbb{R}$, where $f'$, $f''$, $f'''$ denote the iterated one-dimensional \reftext{def:derivative-interior-point-c54-2026b}{derivatives}. Then for all $x,h\in\mathbb{R}$,