newtons_method :: (Fractional a, Ord a)
=> (a -> a) -- ^ The function @f@ whose root we seek
-> (a -> a) -- ^ The derivative of @f@
-> a -- ^ The tolerance epsilon
-> a -- ^ Initial guess, x-naught
-> Maybe a
newtons_method :: (Fractional a, Ord a)
=> (a -> a) -- ^ The function @f@ whose root we seek
-> (a -> a) -- ^ The derivative of @f@
-> a -- ^ The tolerance epsilon
-> a -- ^ Initial guess, x-naught
-> Maybe a