module Task1_2 where

newtonMethod :: (Double -> Double) -> (Double -> Double) -> Double -> Double -> Double
newtonMethod f df x eps
  | abs (xNext - x) < eps = f xNext
  | otherwise             = newtonMethod f df xNext eps
  where xNext = x - (f x) / (df x)


goldenSection :: (Double -> Double) -> Double -> Double -> Double -> Double
goldenSection f a b eps
  | abs (b - a) < eps     = f ((a + b) /2)
  | f xFirst >= f xSecond = goldenSection f xFirst b eps
  | otherwise             = goldenSection f a xSecond eps
  where xFirst  = b - ((b - a) / psi)
        xSecond = a + ((b - a) / psi)
        psi     = (1 + sqrt 5) / 2