Use this theorem: f(x) - p(x) =1/(n+1)! f
(n+1) (
)
(x - x
i) to prove the following.
a) 1/8 h2 M for linear interpolation, where h = x1 - x0 and M = max x0<=x<=x1
| f "(x) |.
b) 1/9√3 h3M for the quadratic interpolation, where h = x1 - x0 = x2 - x1 and
M=maxx0<=x<=x2 | f "(x) |.
c) 3/128 h4M for cubic interpolation, where h = x1 - x0 = x2 - x1 = x3 = x2 and
M = maxx0<= x <=x3 | f "(x) |.
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