Newton's method (Haskell)

Newton.hs

{-# LANGUAGE RankNTypes #-}

import Numeric.Natural (Natural)
import Numeric.AD (diff)

newtonRoot
  :: (Floating a, Ord a)
  => Natural  -- ^ iterations
  -> a        -- ^ epsilon
  -> a        -- ^ starting guess
  -> (forall b. Floating b => b -> b)
  -> Maybe a
newtonRoot i ep x f
   | i == 0 = Nothing
   | abs (f x) - abs ep < 0 = Just x
   | otherwise = newtonRoot (i - 1) ep (x - f x / diff f x) f

main = do
  print $ newtonRoot 100 0.01 2 sin
  print $ newtonRoot 100 0.01 10 (\x -> x**2 - 612)