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.