GATE | GATE CS 1996 | Question 6

The formula used to compute an approximation for the second derivative of a function f at a point X₀ is

(A) A
(B) B
(C) C
(D) D


Answer: (D)

Explanation: The formula used to compute an approximation of the first derivative of an f at a point x0 is

 f'(x0) = (f(x0+h) - f(x0))/h

so an approximation of the second derivative of an f at a point x0 is

f''(x0) = (f'(x0) - f'(x0-h))/h

         =[ ((f(x0+h) - f(x0))/h )- (( f'(x0) - f'(x0-h))/h)]/h

         =[ f(x0+h)-2f(x0)+f(x0-h)] /h^2

Hence , option (D) is correct.

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