Untitled

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

// Function to calculate the derivative of f(x) = 2x^2 + 1 using central difference
double derivative(double x, double h) {
    double result;

    // Central difference formula: f'(x) ˜ (f(x + h) - f(x - h)) / (2 * h)
    result = (2 * pow(x + h, 2) + 1 - (2 * pow(x - h, 2) + 1)) / (2 * h);

    return result;
}

int main() {
    double x, h, result;

    // Input the value of x
    printf("Enter the value of x: ");
    scanf("%lf", &x);

    // Input the step size (h)
    printf("Enter the step size (h): ");
    scanf("%lf", &h);

    // Calculate the derivative
    result = derivative(x, h);

    // Output the result
    printf("The derivative of f(x) = 2x^2 + 1 at x = %.2lf is approximately: %.4lf\n", x, result);

    return 0;
}