I was reading a book and I have found this. If $f(x)=L(x)+R(x)$, with $L$ the quadratic interpolation with three points $x_0, x_1$ and $x_2$, It has been said that it must be true that $$R(x)=\dfrac{f'''(\epsilon(x))}{6} (x-x_0)(x-x_1)(x-x_2),$$ for some $x_0<\epsilon(x)<x_2$, and $$R'(x)=\dfrac{f^{(4)}(\mu)}{24} (x-x_0)(x-x_1)(x-x_2)+\dfrac{f'''(\epsilon(x))}{6}D((x-x_0)(x-x_1)(x-x_2))$$ where D is the derivative operator and $\mu$ was not described.
How can I prove it?