Solution 3 (c).

Investigate the error for the Lagrange interpolation polynomial ,  of degree n = 4.

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

Use formula (iv).       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  0.0000157713.  After all, it is an error bound.  

(c) John H. Mathews 2004