This example illustrates the dangers of picking a poor starting point,
one relatively far from the root.  Note that iterating from 0 is 
impossible (division by zero).  Iterating from -1 also gives wonky behaviour.

Iterating from 1, -2, -3 or -4 gives quick convergence.


 2.000000000000000000
 1.169815477487221478
  .357149517115751899
-1.835679335890070815
-4.505093832444827674  <<< relatively far from root and f' close to zero
 -.043640880622785036  <<< very close to problem point 0
23.930484215614439965      the grand tour continues
22.930484215562109153
21.930484215538255219
20.930484215854862270
19.930484216961118040
18.930484217871193078
17.930484212370250497
16.930484189487252676
15.930484162917787555
14.930484253956713380
13.930484717696496547
12.930485407189078200
11.930484005897337486
10.930474795005322990
 9.930458093473765801
 8.930477095311892615
 7.930656296571728588
 6.931042321320887568
 5.930852736960792660
 4.927434541434775579
 3.918796960235235254
 2.919023936049257771
 1.980365443023475471
 1.152470976239139932
  .336377137744136832 <<< not far from 2nd iteration 
-2.010131876587732107     but by luck a better outcome this time
-3.867790320137767698
-3.031049197542676763
-3.183217037259705302
-3.183063010987051498
-3.183063011933363592 << 36th iteration after a grand tour
-3.183063011933363592