C++ program to find the root of a function using Newton's method

In this program:

f(x) is the function for which you want to find the root, and 

df(x) is its derivative. 

You can replace them with your own function and its derivative.
The newton function implements Newton's method to find the root within a specified tolerance and a maximum number of iterations.
In the main function, you can set the initial guess (initial_guess), tolerance (tolerance), and the maximum number of iterations (max_iterations) to control the root-finding process.

Compile and run this program, and it will find an approximate root of the function using Newton's method. 

#include <iostream>

#include <cmath>

using namespace std;

// Define the function for which we want to find the root

double f(double x) {

    return x * x - 4; // Example function: f(x) = x^2 - 4

}

// Define the derivative of the function

double df(double x) {

    return 2 * x; // Derivative of f(x) = x^2 - 4 is f'(x) = 2x

}

// Newton's method to find the root of a function

double newton(double initial_guess, double tol, int max_iterations) {

    double x = initial_guess;

    int iterations = 0;

    while (iterations < max_iterations) {

        double fx = f(x);

        double dfx = df(x);

        if (abs(fx) < tol) {

            return x; // Found a root within tolerance

        }

        x = x - fx / dfx; // Newton's iteration formula

        iterations++;

    }

    cout << "Newton's method did not converge within the specified number of iterations." << endl;

    return NAN; // Not a number (indicating an error)

}

int main() {

    double initial_guess = 2.0; // Initial guess for the root

    double tolerance = 0.0001; // Tolerance for the solution

    int max_iterations = 100; // Maximum number of iterations

    double root = newton(initial_guess, tolerance, max_iterations);

    if (!isnan(root)) {

        cout << "Approximate root: " << root << endl;

    }

    return 0;

}