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Math Help - Newtons Method

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    Newtons Method

    Use Newton's method to approximate a root of the equation 5 x^7 + 5 x ^4+ 2 =0 as follows.
    Let x_1 = 2 be the initial approximation.
    The second approximation x_2 is
    and the third approximation x_3 is

    Can someone give me some help on this
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  2. #2
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    Quote Originally Posted by dat1611 View Post
    Use Newton's method to approximate a root of the equation 5 x^7 + 5 x ^4+ 2 =0 as follows.
    Let x_1 = 2 be the initial approximation.
    The second approximation x_2 is
    and the third approximation x_3 is

    Can someone give me some help on this
    this is just an iteration of a well known formula ... I suggest you research it.

    Pauls Online Notes : Calculus I - Newton's Method
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    can someone give me an example
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    MHF Contributor chisigma's Avatar
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    Each Newton's iteration is...

    \displaystyle x_{n+1} = x_{n} - \frac{f(x_{n})}{f^{'} (x_{n})} (1)

    In Your case is...

    f(x) = 5\ x^{7} + 5\ x^{4} + 2

    f^{'} (x) = 35\ x^{6} +20 \ x^{3} (2)

    ... so that setting x_{1} = 2 in (2) and then evaluating (1) You obtain x_{2} = 1.6991166....... then You set x_{2} in (2) and then evaluate (1) and obtain x_{3}... then...

    Kind regards

    \chi \sigma
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