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The OP asks for a "reputable source", I would think that Press and Teukolsky's Numerical Recipes qualifies as such. As they explain, if you approximate $f'(x)\approx h^{-1}[f(x+h)-f(x)]$ the truncation error (from higher order terms in the Taylor expansion) is of first order in the small increment $h$. You can improve this to a truncation error of second order by symmetrizing, $f'(x)\approx (2h)^{-1}[f(x+h)-f(x-h)]$.