Solution 3 (b).

Investigate the error for the Lagrange interpolation polynomial ,  of degree n = 3.

Looking at the above graph we make the following estimate for the error:

Use formula (iii).       is valid for  ,  and find the error bound for this example.  

Thus,     is valid for  ,  which is a little bit larger than the maximum error  0.000463413.  After all, it is an error bound.  

(c) John H. Mathews 2004