Question

Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y =(x − 5)^2 that is closest to the origin.

Answer 1

y' = 2(x-5)

Let x0=1
x1 = 1 - y/y' = 1 - 16/-8 = 3
x2 = 3 - 4/-4 = 4
x3 = 4 - 1/-2 = 6
x4 = 6 - 1/2 = 5.5
and so on for six decimal places.