Taylor table for 4th order approximations of the second order derivative

Objective: In this question, we need to find 4th order approximations of the second order derivative. 1.Central difference: from the concept of Taylor\'s table, we know that, ∂2u/∂x2 = af(i-2)+bf(i-1)+cf(i)+df(i+1)+ef(i+2) we need to find the coefficients from the above equations from taylors table, f(i) ∆xf’(x)…