A continuous function f(x) is defined. If the third derivative at xi is to be computed by using he fourth order central finite divided difference scheme (with step length = h) the correct formula is

• A. \(f'''\left( {{x_i}} \right) = \frac{{ - f\left( {{x_{i + 3}}} \right) + 8f\left( {{x_{i + 2}}} \right) - 13f\left( {{x_{i + 1}}} \right) + 13f\left( {{x_{i - 1}}} \right) - 8f\left( {{x_{i - 2}}} \right) + f\left( {{x_{i - 3}}} \right)}}{{8{h^3}}}\)
• B. \(f'''\left( {{x_i}} \right) = \frac{{f\left( {{x_{i + 3}}} \right) - 8f\left( {{x_{i + 2}}} \right) - 13f\left( {{x_{i + 1}}} \right) + 13f\left( {{x_{i - 1}}} \right) + 8f\left( {{x_{i - 2}}} \right) + f\left( {{x_{i - 3}}} \right)}}{{8{h^3}}}\)
• C. \(f'''\left( {{x_i}} \right) = \frac{{ - f\left( {{x_{i + 3}}} \right) - 8f\left( {{x_{i + 2}}} \right) - 13f\left( {{x_{i + 1}}} \right) + 13f\left( {{x_{i - 1}}} \right) + 8f\left( {{x_{i - 2}}} \right) + f\left( {{x_{i - 3}}} \right)}}{{8{h^3}}}\)
• D. \(f'''\left( {{x_i}} \right) = \frac{{f\left( {{x_{i + 3}}} \right) + 8f\left( {{x_{i + 2}}} \right) - 13f\left( {{x_{i + 1}}} \right) + 13f\left( {{x_{i - 1}}} \right) - 8f\left( {{x_{i - 2}}} \right) + f\left( {{x_{i - 3}}} \right)}}{{8{h^3}}}\)