title: find a cube root with Newton's method
body: <p>Newton's method is to find successively better approximations to the roots of polynominal.<br>
  I have learned to find square root like:</p>
  
  <pre><code>    from sys import argv
      script, k,epsilon  = argv
  
      def find_square_root(k, epsilon):
          guess = k/2
          while abs(guess**2 -k) &gt;= epsilon:
              guess = guess - (guess**2 -k)/(2*guess)
              print(f"Square root of {k} is about {guess}.")
  
      k = float(argv[1])
      epsilion = float(argv[2])
      find_square_root(k, epsilion)
  </code></pre>
  
  <p>Run it and come by:</p>
  
  <pre><code>    $ python3 successive_approximation.py 128 0.001
      Square root of 128.0 is about 33.0.
      Square root of 128.0 is about 18.439393939393938.
      Square root of 128.0 is about 12.690526879310774.Square root of 128.0 is about 11.388395266147043.
      Square root of 128.0 is about 11.31395340237364.
      Square root of 128.0 is about 11.313708501635368.
  </code></pre>
  
  <p>How to find a cube root with Newton's method?</p>