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Engineering Mathematics Question on Total derivative

The second derivative of a function f is computed using the fourth-order Central Divided Difference method with a step length h.
The CORRECT expression for the second derivative is

A

c

B

112h2[fi+2+16fi+1−30fi+16fi+1−fi−2]\frac{1}{12h^2}[f_{i+2}+16f_{i+1}-30f_i+16f_{i+1}-f_{i-2}]

C

112h2[−fi+2+16fi+1−30fi+16fi+1+fi−2]\frac{1}{12h^2}[-f_{i+2}+16f_{i+1}-30f_i+16f_{i+1}+f_{i-2}]

D

112h2[−fi+2−16fi+1+30fi−16fi−1−fi−2]\frac{1}{12h^2}[-f_{i+2}-16f_{i+1}+30f_i-16f_{i-1}-f_{i-2}]

Answer

c

Explanation

Solution

The correct option is (A) : 112h2[−fi+2+16fi+1−30fi+16fi+1−fi−2]\frac{1}{12h^2}[-f_{i+2}+16f_{i+1}-30f_i+16f_{i+1}-f_{i-2}].