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In page Finite difference:
"The main problem[citation needed] with the central difference method, however, is that oscillating functions can yield zero derivative. If f (nh) = 1 for n odd, and f (nh) = 2 for n even, then f ′(nh) = 0 if it is calculated with the central difference scheme. This is particularly troublesome if the domain of f is discrete. See also Symmetric derivative.
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