Construct a program that will request you to input function and will...

Construct a program that will request you to input function and will perform evaluation of all critical points by solving a system of equations and by evaluation of the determinant of the Hessian Matrix will determine local max/min or saddle points.Guidance:-You May use any programming language.-The program shall work with one of the input of the functionsprovided below.-It is not allowed to use ready functions to perform operations except arithmetical.-Derivative should be computed by definition (limit notation).-It is allowed to apply numerical methods for solving system of equations.