Use this tool to quickly find an approximate root of any function using Newton’s Method.

## Newton’s Method Calculator

**Explanation:**

Newton’s Method is an iterative numerical method for finding successively better approximations to the roots (or zeroes) of a real-valued function. The formula to obtain the next approximation (x1) from the current approximation (x0) is given by:

x1 = x0 – f(x0)/f'(x0)

**How to use this calculator:**

- Enter the function f(x) that you want to find the root of in the “Function f(x)” field.
- Enter the derivative f'(x) of the function in the “Derivative f'(x)” field.
- Provide an initial guess for the root in the “Initial Guess (x0)” field.
- Click on the “Calculate” button to find the approximation of the root.

**How it calculates the results:**

The calculator uses your function, its derivative, and the initial guess to apply Newton’s Method. The result displayed is the approximation of the root after a fixed number of iterations or when the approximation improvement falls below a certain threshold.

**Limitations:**

Newton’s Method may not converge if the function is not well-behaved near the initial guess or if the initial guess is not close enough to the true root. Additionally, it may also fail if the function has a horizontal tangent (where f'(x) is 0) near the root.