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Math Help - Finding the value of N for Simpson's Rule

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by johnley View Post
    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.
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