newton.root <- function(f, x0 = 0, tol = 1e-9, max.iter = 100) {
  # initialise
  x <- x0
  fx <- ftn(f, x)
  iter <-  0
  # continue iterating until stopping conditions are met
  while ((abs(fx$f) > tol) && (iter < max.iter)) {
    x <- x - fx$f/fx$fgrad
    fx <- ftn(f, x)
    iter <-  iter + 1
    cat("At iteration", iter, "value of x is:", x, "\n")
  }
  
  # output depends on success of algorithm
  if (abs(fx$f) > tol) {
    cat("Algorithm failed to converge\n")
    return(NULL)
  } else {
    cat("Algorithm converged\n")
    return(x)
  }
}
# f <- function(x) x^2 - 5
# f <- expression(abs(x) ^ 0.5)
# f <- function(x) x*exp(-x^2) - 0.4*(1/(exp(x)+1)) - 0.2
# f <- function(x) x^3 -2*x^2 - 11*x + 12
f <- function(x) 2*x^3+ 3*x^2 + 5
ftn <- function(f, x){
  df <- deriv(f, 'x', func = TRUE)
  dfx <- df(x)
  f <- dfx[1]
  fgrad <- attr(dfx, 'gradient')[1,]
  return(list(f = f, fgrad = fgrad))
}
newton.root(body(f), 2.35284172)
curve(f,-5,5)
abline(h = 0, col=2, lty = 3)