1. ## 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

2. distance between $(x, x^2)$ and $(4,0)$ is

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

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

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

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

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