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GATE | GATE CS 1996 | Question 6

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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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Last Updated : 02 Jun, 2021
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