Let $\displaystyle f:[ a,b]\rightarrow \mathbb{R}$ be a continuous function, that is $\displaystyle f\in \mathcal{C}[ a,b]$. It is to be proven that $\displaystyle m\in \mathcal{C}[ a,b]$, where $\displaystyle m( x) =\min_{a\leq t\leq x} \ f( t)$. Claim: $\displaystyle m$ is a monotonically decre...
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