The Newton-Raphson Method for Root-finding

Go go go! Along with the tangent lines!

oopt = ani.options(ani.height = 500, ani.width = 600, outdir = getwd(), nmax = 100,
    interval = 1, title = "Demonstration of the Newton-Raphson Method",
    description = "Go along with the tangent lines and iterate.")
ani.start()
par(mar = c(3, 3, 1, 1.5), mgp = c(1.5, 0.5, 0), pch = 19)
newton.method(function(x) 5 * x^3 - 7 * x^2 - 40 *
    x + 100, 7.15, c(-6.2, 7.1), main = "")
ani.stop()
ani.options(oopt)