Hi,
I derive the Lagrange form of the remainder by using the Weighted Mean-Value theorem on the integral form of the remainder.
The integral form according to my Calculus book is,
The Lagrange form is,
If I create a Lagrange polynomial out of two points and ,
then according to my Numerical Analysis book the Lagrange form of the remainder is,
,
which to me makes more sense since we should take into account all points when calculating the remainder.
Please let me know if this question does not make sense and I will try and rephrase.
Thanks.