Chapter 13, Problem 12P

Develop a program using a programming or macro language to implement the golden-section search algorithm. Design the program so that it is expressly designed to locate a maximum. The subroutine should have the following features:

• Iterate until the relative error falls below a stopping criterion or exceeds a maximum number of iterations.

• Return both the optimal x and $f\left(x\right)$.

• Minimize the number of function evaluations.

Test your program with the same problem as Example 13.1.