= Duffin-Schaeffer polynomial derivative inequality
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{title2=$\|p^{(k)}\|_\infty\le T_n^{(k)}(1)$}
= Markov-Duffin-Schaeffer theorem
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{synonym}
If a real degree-at-most-$n$ <polynomial> has absolute value at most one at every extremum $\cos(j\pi/n)$ of the <Chebyshev polynomial> $T_n$, its $k$th <derivative> on $[-1,1]$ is bounded by $T_n^{(k)}(1)$, for $1\le k\le n$. This strengthens the <Markov inequality for polynomial derivatives> by replacing a bound on the whole interval with these finitely many samples. The node set is rigid, as quantified by <uniqueness of Chebyshev derivative-norming nodes>.
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