Untitled

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

// Define the function and its derivative
double f(double x) {
    return x * x * x - 5 * x + 3;
}

double df(double x) {
    return 3 * x * x - 5;
}

// Newton-Raphson using divided differences formula
double newtonRaphson(double x0, double tolerance, int maxIterations) {
    double x = x0;
    int iterations = 0;

    while (iterations < maxIterations) {
        double fValue = f(x);
        double dfValue = df(x);
        
        double h = fValue / dfValue;
        double h2 = h * h;
        double h3 = h * h2;

        x -= h - 0.5 * h2 + h3 / 6;

        if (fabs(h) < tolerance) {
            printf("Converged to root after %d iterations.\n", iterations);
            return x;
        }

        iterations++;
    }

    printf("Failed to converge after %d iterations.\n", maxIterations);
    return x;
}

int main() {
    double initialGuess = 1.0;
    double tolerance = 1e-6;
    int maxIterations = 1000;

    double root = newtonRaphson(initialGuess, tolerance, maxIterations);

    printf("Approximate root: %lf\n", root);

    return 0;
}