Example 3.  Compare the secant method with the inverse quadratic method for finding the roots of the cubic polynomial  .  

3 (b)  Investigate slow convergence at the double root  .  

Solution 3 (b).

Graph the function.

Slow Convergence.  Investigate slow convergence at the double root  ,  using the starting values  

Use the subroutine for the inverse quadratic method.  

Compare with the slightly slower secant method.

(c) John H. Mathews 2005