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

Base it on two initial guesses, and have the program generate the third initial value at the midpoint of the interval.

Check whether the guesses bracket a maximum. If not, the subroutine should not implement the algorithm, but should return an error massage.

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

Return both the optimal x and ƒ(x).

Minimize the number of function evaluations.

Test your program with the same problem as Example 13.2