This problem considers a direct proof of Theorem 5.9, at least for the case of when = 1. This will help demonstrate how this result is independent of the coefficients of the polynomial. (a) If 1() =...

This problem considers a direct proof of Theorem 5.9, at least for the case of when

= 1. This will help demonstrate how this result is independent of the coefficients of the polynomial.

(a) If

₁() =
+

₀, explain why

(b) Sketch the two absolute values in part (a) as a function of b0. Use this to explain why max_−1≤x≤1
|
₁()| =1+ |
₀|. From this derive the result stated in the theorem.