Solution
= Solution
The recurrence $T_{k+1}=2xT_k-T_{k-1}$ shows that $T_{n+1}$ has leading coefficient $2^n$. Since its roots are the interpolation nodes, $T_{n+1}=2^n\Pi$, and $|T_{n+1}|\le1$ on $[-1,1]$.
= Solution
The recurrence $T_{k+1}=2xT_k-T_{k-1}$ shows that $T_{n+1}$ has leading coefficient $2^n$. Since its roots are the interpolation nodes, $T_{n+1}=2^n\Pi$, and $|T_{n+1}|\le1$ on $[-1,1]$.