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Thread: Newton Method

  1. #1
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    Unhappy Newton Method

    Hi heres my question.

    Use Newton’s Method to approximate the coordinates (x,y) of the point on the parabola y=x^2 that is closest to the point (4,0).

    Round all answers to 2 decimal places

    Thanks for the help
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  2. #2
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    distance between $\displaystyle (x, x^2)$ and $\displaystyle (4,0)$ is

    $\displaystyle d = \sqrt{(x-4)^2 + (x^2 - 0)^2}$

    distance will be a minimum, when the radicand function, $\displaystyle (x-4)^2 + (x^2 - 0)^2$ , is a minimum. so, let

    $\displaystyle f(x) = (x-4)^2 + x^4$

    $\displaystyle f'(x) = 2(x-4) + 4x^3$

    distance will be a minimum when $\displaystyle f'(x) = 0$ , and this is the function with which you want to use Newton's method.
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