// ConsoleApplication31.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include <iostream>
#define _USE_MATH_DEFINES
#include "math.h"

using namespace std;


double f(double x)
{
	return exp(-0.5 * x) * sin(5 * M_PI * x);
}


double xi(double x, int i, double h)
{
	return x + i * h;
}

double FPrimRSP(double x, double h)
{
	return (-1 * f(xi(x, 2, h)) + 4 * f(xi(x, 1, h)) - 3 * f(x)) / (2 * h);
}

double FBisRSP(double x, double h)
{
	return (-1 * f(xi(x, 3, h)) + 4 * f(xi(x, 2, h)) - 5 * f(xi(x, 1, h)) + 2 * f(x)) / pow(h, 2);
}

double FTerRSP(double x, double h)
{
	return (-3 * f(xi(x, 4, h)) + 14 * f(xi(x, 3, h)) - 24 * f(xi(x, 2, h)) + 18 * f(xi(x, 1, h)) - 5 * f(x)) / (2 * pow(h, 3));
}

double FPrimRST(double x, double h)
{
	return (3 * f(x) - 4 * f(xi(x, -1, h)) + f(xi(x, -2, h))) / (2 * h);
}

double FBisRST(double x, double h)
{
	return (2 * f(x) - 5 * f(xi(x, -1, h)) + 4 * f(xi(x, -2, h)) - f(xi(x, -3, h))) / pow(h, 2);
}

double FTerRST(double x, double h)
{
	return (5 * f(x) - 18 * f(xi(x, -1, h)) + 24 * f(xi(x, -2, h)) - 14 * f(xi(x, -3, h)) + 3 * f(xi(x, -4, h))) / (2 * pow(h, 3));
}

double FPrimRSC(double x, double h)
{
	return (f(xi(x, 1, h)) - f(xi(x, -1, h))) / (2 * h);
}

double FBisRSC(double x, double h)
{
	return (f(xi(x, 1, h)) - 2 * f(x) + f(xi(x, -1, h))) / (pow(h, 2));
}

double FTerRSC(double x, double h)
{
	return (f(xi(x, 2, h)) - 2 * f(xi(x, 1, h)) + 2 * f(xi(x, -1, h)) - f(xi(x, -2, h))) / (2 * pow(h, 3));
}

int main()
{
	double h = 1.e-3;
	double x;

	cout << "Podaj x: " << endl;
	cin >> x;
	cout << "RSP" << endl;
	cout << "F'(" << x << ")" << "\t" << FPrimRSP(x, h) << endl;
	cout << "F''(" << x << ")" << "\t" << FBisRSP(x, h) << endl;
	cout << "F'''(" << x << ")" << "\t" << FTerRSP(x, h) << endl;
	cout << "RST" << endl;
	cout << "F'(" << x << ")" << "\t" << FPrimRST(x, h) << endl;
	cout << "F''(" << x << ")" << "\t" << FBisRST(x, h) << endl;
	cout << "F'''(" << x << ")" << "\t" << FTerRST(x, h) << endl;
	cout << "RSC" << endl;
	cout << "F'(" << x << ")" << "\t" << FPrimRSC(x, h) << endl;
	cout << "F''(" << x << ")" << "\t" << FBisRSC(x, h) << endl;
	cout << "F'''(" << x << ")" << "\t" << FTerRSC(x, h) << endl;

	system("PAUSE");

	return 0;
}