The formula used to compute an approximation for the second derivative of a…
1996
The formula used to compute an approximation for the second derivative of a function f at a point x0 is:
- A.
(f(x0 + h) + f(x0 - h)) / 2
- B.
(f(x0 + h) - f(x0 - h)) / (2h)
- C.
(f(x0 + h) + 2f(x0) + f(x0 - h)) / h^2
- D.
(f(x0 + h) - 2f(x0) + f(x0 - h)) / h^2
Show answer & explanation
Correct answer: D
In the Taylor expansion about x0, the first-derivative terms in f(x0 + h) and f(x0 - h) cancel when the two expressions are added. Subtracting 2f(x0) leaves h^2 times the second derivative at x0, plus higher-order terms. Therefore the central second-difference approximation is (f(x0 + h) - 2f(x0) + f(x0 - h)) / h^2. Hence option 4 is correct.