Example 2.  Find the minimum of the function    on the interval    using the cubic search method.

Solution 2.

Set , and determine the first value of  h and use it to compute .  
Observe that the algorithm is not a bracketing method and   does not lie in the given interval  .  

Now compute the values    and  .

Now set    and continue the iteration process.  
The list of computations are obtained by using the CubicSearch subroutine are:  

Let us compare these answers with Mathematica's subroutine FindMinimum.

The value of the function at    is  ,  which compares favorably with the minimum value found by the Secant Method for finding the root of  .  The values obtained by the Secant Method are included below for comparison purposes.

(c) John H. Mathews 2004