Remark: It is difficult to improve the bound given in (2.9) for the error, but we can instead look for an estimate of the error:
Error Estimate
Suppose that has a second derivative which is continuous and bounded in the region R. Under this hypothesis, the third derivative of exists, and we may write
(2.10)
where . Subtracting this from the corresponding relation satisfied by the approximate values,
has a second derivative which is continuous and bounded in the region R. Under this hypothesis, the third derivative of 
exists, and we may write 
. Subtracting this from the corresponding relation satisfied by the approximate values, 
