In this question we will investigate the number of intervals

Last updated: 3/3/2023

In this question we will investigate the number of intervals necessary to achieve a given level of accuracy using Simpson s method To make the project concrete we focus on the integra dz I a Let f x Find the fourth derivative of f x b Which of the following best describes the behaviour of f 4 z on the interval 1 1 7 O Increasing Decreasing Sometimes increasing sometimes decreasing c What is the maximum value of f 4 z on the interval 1 1 7 max f x 15 51 7 13 in an equivalent form where n need not be an integer d Let L denote the value found above Taking a 1 and b 1 7 and assuming n 0 isolate n to express the inequality L b a 1 S 180 n 107 n H e Use the results above to find the smallest even integer n for which 1 1 7 1