# 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 $$\Delta t$$?