Let $I$ be an interval in the sense of \ref{def:interval-real-line-c54-2026a}, let $[a,b]\subseteq I$ with $a<b$, and let $f:I\to\mathbb{R}$ be continuous on $[a,b]$ in the sense of \ref{def:continuity-closed-interval-c54-2026a}. Then there exist points $x_{\min},x_{\max}\in[a,b]$ such that