GATE Civil Engineering
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A continuous function $f(x)$ is defined. If the third derivative at $x_i$ is to be computed by using the fourth order central finite-divided-difference scheme (with step length $=h$), the correct formula is

  1. $f^{’’’}(x_i)={\large\frac{-f(x_{i+3})+8f(x_{i+2})-13f(x_{i+1})+13f(x_{i-1})-8f(x_{i-2})+f(x_{i-3})}{8h^3}} \\$
  2. $f^{’’’}(x_i)={\large\frac{f(x_{i+3})-8f(x_{i+2})-13f(x_{i+1})+13f(x_{i-1})+8f(x_{i-2})+f(x_{i-3})}{8h^3}} \\$
  3. $f^{’’’}(x_i)={\large\frac{-f(x_{i+3})-8f(x_{i+2})-13f(x_{i+1})+13f(x_{i-1})+8f(x_{i-2})-f(x_{i-3})}{8h^3}} \\$
  4. $f^{’’’}(x_i)={\large\frac{f(x_{i+3})-8f(x_{i+2})+13f(x_{i+1})+13f(x_{i-1})-8f(x_{i-2})-f(x_{i-3})}{8h^3}}$
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