User:Yongtao-Li/NM.HW4.4

=Problem 4.4 "Another step in the proof of Simple Simpson's Error Theorem"=

Given
In order to prove Simple Simpson's Error Theorem, we define

Find
The third derivative of (4.4.1)

Solution
From Problem 4.2, we have the first derivative of (4.4.1):

Then we can compute the second derivative of (4.4.1) use the above equation (4.4.2)

At last we can get the third derivative of (4.4.1) use the above equation (4.4.3)