I'm learning some Numerical Analysis but this is a very calculus-like question so I'll put it here.
Forward/Backward - Difference formula,
is continuous on and exists for all .
and for such that .
is also in .
Since I do not have any information on f , the error in my approximation is bounded by where is the maximum value of on my interval. How can I find the error bound without actually taking the second derivative of ?