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Math Help - newtons method

  1. #1
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    newtons method

    Use Newton's method to approximate the root of the equation

    x^3=113 x+226

    that belongs to the interval (6,12 ).

    Start with x0=12 and perform three iterations, i.e., find x1,x2, and x3.

    Calculate |x0−x1|,|x1−x2|, and |x3−x2|.

    1. Use Newton's method

    where the function f has a positive leading coefficient so that f(x)= ???
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  2. #2
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    define f(x)=x^3-113x-226=0

    Find f'(x).

    Hence evaluate

    x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} for n=0,1,2.
    Last edited by scorpion007; October 22nd 2009 at 10:30 PM. Reason: fixed 'n'
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  3. #3
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    Use the equations right?
    So x1=12-[f(12)/f'(12)], then x2=x1-[f(x1)/f'(x1)] and so on..
    Is that what you were asking for?
    With
    f(x)=-x^3+113x+226
    f'(x)=-3x^2+113
    Then it's just simple substitution from there.
    Last edited by endling; October 22nd 2009 at 08:10 PM. Reason: xn+1=xn-[f(x1)/f'(x1)], not plus, thanks to scorpion007
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  4. #4
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    Quote Originally Posted by endling View Post
    Use the equations right?
    So x1=12-[f(12)/f'(12)], then x2=x1-[f(x1)/f'(x1)] and so on..
    Corrections in red.
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  5. #5
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    Quote Originally Posted by scorpion007 View Post
    Corrections in red.
    Oh, sorry, yes, you are correct. It's a bit late into the evening for me x___x
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  6. #6
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    thank you both so much, i got it now
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