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Homework Help: Finding critical values of a function

  1. Mar 1, 2010 #1
    1. The problem statement, all variables and given/known data
    Use Newton's Method to find the critical numbers of the function f(x) = 2x^5 - 5x^2 - 20x + 12 correct to three decimal places

    2. Relevant equations

    3. The attempt at a solution
    f'(x) = 10x^4-10x-20
    = 10(x^4-x-2)
    = 10(x+1)(x^3-x^2+x-2)

    I'm not really sure what Newton's method is, so I just tried factoring the derivative, but I can't factor it any further and I don't know what to do from here. HELP!
  2. jcsd
  3. Mar 1, 2010 #2
    Wikipedia is your friend:


    Well you clearly have one critical point which you don't have to estimate. As for the x^3 - x^2 + x - 2 factor, the discriminant of this is negative, and you have two complex roots and a real root. You can disregard the complex roots. If g(x) = x^3 - x^2 + x - 2, then f(1) = -1 and g(2) = 4, which implies that the remaining real root is between x = 1 and x = 2. Now see if you can garner any useful information for approximating this root from the wikipedia article.
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