Is it mandatory to use the forward and the backward interpolation formula in order to interpolate a function at the respective locations towards the beginning and at the end of the given data set? Justify with proper reasons.
If $x_0,x_1,x_2,\dots,x_n$ are the interpolating points, then Newton forward difference method is better for points which are closer beginning of the table, while Newton backward difference method is better for points which are closer to the end of the table.
Please give a proper justification wrt the question.