Chapter 4 - Section 1 - Question 10

Use Newton’s Method to approximate all roots of the given functions accurate to 3 places after the decimal If an interval is given find only the toos that lie in the interval.

I am going to do this using the animation package by Yihui Xie one of the great God’s of modern R packages. Within this package is a function called newton.method()

require(animation)
#fun <- function(x) {x^17 - 2*x^13 - 10*x^8 +10}
newton.method( FUN = function(x) x^17 - 2*x^13 - 10*x^8 +10, init = -2, rg = c(-2,2), tol = 0.001, interact= FALSE)

newton.method( FUN = function(x) x^17 - 2*x^13 - 10*x^8 +10, init = 2, rg = c(2,-2), tol = 0.001, interact= FALSE)