... Hi(x) 0 1 1 1 1 x 1-x 2x 2 (3x2 -1 )/2 ( 2-4 x+x2)/2 2(2x2 -1 ) 3 x(5x2 -3 )/2 ( 6-1 8x+9x2-x3)/6 4x(2x2 -3 ) 4 (35x4 -3 0x2+3)/8 (2 4-9 6x+72x2 -6 x3+x4)/24 4(4x4 -1 6x2+3) Like ... yielding f(x0 -2 h )-8 f(x0-h)+8f(x0+h)-f(x0+2h) = ─12hf'(x0)+R(h5 )- ~R(h5) , (4.1.13) and solving for f'(x0) we get. f'(x0) = [f(x0 -2 h) ─ 8f(x0-h) + 8f(x0+h) ... (1970) Harper and Row, New York. 3. Stoer, J. and Bulirsch, R., "Introduction to Numerical Analysis& quot; (1980), Springer-Verlag, New York, §2.2. 4. Gradshteyn, I.S. and Ryzhik,I.M.,...