Quiz 2: Error term in the Taylor Series

The fourth order centered difference formula you just say for the first derivative was:

\[\frac{-T(t_{i+2})+8T(t_{i+1})-8T(t_{i-1})+T(t_{i-2})}{12\Delta t} = T^\prime(t_i) + {\cal O}((\Delta t)^4)\]

Without explicitly writing out the Taylor series for all of the terms in this formula, can you determine what derivative of T(t) will appear in the error term, multiplying \(\Delta t\)?

Possible answers:

1. Third derivative

2. Fourth derivative

3. Fifth derivative

• Hint