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Math Help - Newtons Method Help

  1. #1
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    Newtons Method Help

    Using newtons method, solve the equation, x^3-4x-12=0 accuratey to six decimal places?

    Im having extreme troubles with this can anyone please help
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  2. #2
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    Quote Originally Posted by NoAsherelol View Post
    Using newtons method, solve the equation, x^3-4x-12=0 accuratey to six decimal places?

    Im having extreme troubles with this can anyone please help

    Newton's method uses the recursion:

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

    to find a root of f(x)=0, so here we put:

    f(x)=x^3-4x-12

    f'(x)=3x^2-4

    Then:

    x_{n+1}=x_n-\frac{x_n^3-4x_n-12}{3x^2-4}

    Now we need a guess to get us started, we observe that f(x) is negative at x=2 and positive at x=3 (and nearer to zero at x=3) so we take x_0=3 as our starting value.

    You will find this converges to the required accuracy after about 3 itterations.

    RonL
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