The question then goes on to ask for the upper bounds from trapezoid and simpsons rule but the book has different answers then I am getting. Did I do the first one correctly?
now the question asks to find the number n of subintervals that will make the error less than
just typing out the midpoint because the book is giving not the same answer I am giving
I am getting n= 9 book is saying n = 24
re your first post on this thread
BobP is correct. The max of the absolute value of the 2nd derivative is 1/4 at x=0 which leads to the bound of 9/3200
your 2nd problem is wrong for the same reason. The max value is 1/4 not 1/32
To reiterate what romsek and BobP are saying:
You are taking , which is the absolute value of the maximum of the second derivative on the given interval. BobP and romsek are saying, take the absolute value function first: . Then, find the maximum. Hence, .