remember K is the maximum of the absolute value of f^4(x)
So you are correct here you use 3.
My question is really just a clarification. When using the Simpson's error equation to determine the value of n needed to produce a certain level of accuracy, you take the maximum absolute value, right? So for instance, that means that for this problem:
with
the maximum value of on [-1,2] is the minimum of the function on that interval, at x = 0. So for
you use K = 3, right? Or do you use the actual maximum itself? (In the example, about at x = 0.866 or -0.886.) Thanks for the help!
You may wonder why if you know the max is 3 why use a bigger number?
Since we are no longer in the middle ages typically we can graph
|f^4(x)| and with out zooming and tracing we can simply pick an obvious upper bound so that we don't need the exact max.
For eg with Mathcad once we define f(x) we don't even need to calculate
f^4(x) we simply plot |f^4(x)| and pick an obvious upper bound.
In the old days when processors were run by gerbels we were more concerned with n being as small as possible and so we spent more time
trying to find the smallest n instead of any n which would give us the desired accuracy