# Finding the value of N for Simpson's Rule

• Oct 13th 2009, 01:51 PM
johnley
Finding the value of N for Simpson's Rule
Find a value of N such that Simpson's Rule approximates

5
∫x^-1/4 dx
2

with an error of at most 10^-2 (but don't calculate Simpson's Rule).

The answer sheet says the answer is 4, but I cant get that answer. So far all I found was the fourth derivative.

fourth derivative = 585/256 x^(-17/4)

In class, we took a similar problem and graphed the fourth derivative to see where it was even to and plugged the value in for the derivative to find the k4, but I tried to do this, and I got a huge number not even close to 4.

Can anyone help me out, please?
• Oct 13th 2009, 07:40 PM
mr fantastic
Quote:

Originally Posted by johnley
Find a value of N such that Simpson's Rule approximates

5
∫x^-1/4 dx
2

with an error of at most 10^-2 (but don't calculate Simpson's Rule).

The answer sheet says the answer is 4, but I cant get that answer. So far all I found was the fourth derivative.

fourth derivative = 585/256 x^(-17/4)

In class, we took a similar problem and graphed the fourth derivative to see where it was even to and plugged the value in for the derivative to find the k4, but I tried to do this, and I got a huge number not even close to 4.

Can anyone help me out, please?

Find the largest positive integer solution of $\frac{(b-a)^3}{12 n^2} \, \text{max}_{[a, b]} f''(x) \leq \frac{1}{100}$ where $a = 2, \, b = 5, \, f(x) = x^{-1/4}$ and $\text{max}_{[a, b]} f''(x)$ is the maximum value of f(x) over the interval [a, b] of integration.