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.