Ruby implementation of the Newton's method (https://en.wikipedia.org/wiki/Newton%27s_method)

newtons_method.rb

class NewtonsMethod
  def initialize(f_proc, f_prime_proc)
    @fp = f_proc
    @fpp = f_prime_proc
  end

  def apply(x)
    x - (@fp.call(x) / (@fpp.call(x) * 1.0))
  end

  def solve(x, steps)
    x1 = apply(x)
    r = @fp.call(x1)
    s = steps - 1
    return x1 unless s > 0 || r.zero?
    solve(x1, s)
  end
end

f = ->(x) { -4 * (x**3) - 2 * (x**2) - 2 * x - 3 }
fp = ->(x) { -12 * (x**2) - 4 * x - 2 }

nm = NewtonsMethod.new(f, fp)
nm.solve(-2, 2)
#  => -1.0582629570422042