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

3 (a)  Investigate fast convergence at the simple root  .  

Solution 3 (a).

Graph the function.

Fast Convergence.  Investigate fast convergence at the simple root  ,  using the starting values  

Use the subroutine for the inverse quadratic method.  

Use the efficient version for the inverse quadratic method.  

Compare with the slower secant method.

(c) John H. Mathews 2005