/*
 * Author: Moshe Moshonov
 * Email: moshemosh@mail.tau.ac.il
 * Date: 08/03/2015
 * ID: 123456789
 *
 * Short Description:
 * This program computes a 1st order derivative of a function using a central 
 * difference scheme.
 * The function is chosen to be a simple exponent.
 *
 * Compilation: g++ my_simple_program.cpp -lm -o my_simple_program
 * Execute in Shell: ./my_simple_program
 */

#include <stdio.h>
#include <math.h>

/*
 * This function computes the value of function f at point x and returns the 
 * result.
 *
 * Parameters:
 * x - Point to evaluate function.
 */
double f(double x)
{
	return exp(x);
}

/*
 * This function computes the 1st order derivative of function f at point x and returns the 
 * result.
 *
 * The derivative is computed using a central difference scheme:
 * f(x + dx) - f(x - dx)
 * ---------------------
 *        2 * dx
 *
 * Parameters:
 * x - Point to evaluate derivative.
 * dx - Step size to use for approximation (After Taylor expansion).
 */
double df_dx(double x, double dx)
{
	return (f(x + dx) - f(x - dx)) / (2.0 * dx);
}

int main()
{
	/* Point to compute f' at. */
	double x = 2.0;
	/* Step size for approximation. */
	double dx = 0.0001;
	
	printf("f = exp(x)\n\n");
	printf("f'(%.7f) = ?\n", x, df_dx(x, dx));
	printf("Approximate: %.7f\n", df_dx(x, dx));
	printf("Analytic: %.7f\n", f(x));

	return 0;
}