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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Last Updated :
02 Jun, 2021
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