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
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.