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Mar 1 2016 12:33am
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Mar 1 2016 10:12am
http://www.geometrictools.com/Documentation/FiniteDifferences.pdf

This should help you, I'm at work currently but I'll take a peak later when I'm off.
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Mar 1 2016 11:47am
Use Taylor theorem with Lagrange remainder :

f(a+h) = f(a) + h.f '(a) + h²/2 . f '' (a) + h^3/6 . f ''' (t1), where t1 is between a and a+h ;
f(a-h) = f(a) - h.f '(a) + h²/2 . f '' (a) - h^3/6 . f ''' (t2), where t2 is between a-h and a.

Simplify e(h) with the given formulaes :

e(h) = (h²/12) . ( f '''(t1) + f '''(t2) )

Use triangle inequality :

|e(h)| ≤ h².2M / 12
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