Let $I = [a,b]$ be a real closed interval. Let $n$ be a positive integer and let $x_i = a+i\frac{(b-a)}{n}$ for $i=0,...,n$. Let $p_j(x)$ be the Lagrange interpolating polynomial of the $n+1$ points of coordinates $(x_i, \delta_{ij})$. The polynomial $p_j(x)$ behaves well but there exists a certain $d$ such that for all $x$ with $|x-x_j| >d$ the values of $p_j(x)$ start to oscillate a lot. Is it possible to express $d$ as a function of $a$, $b$ and $n$?
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