Newton's Method in Calculus | Formula, Equation & Examples

MathVibes on Instagram: "In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a real-valued function f, its derivative f′, and an initial guess x₀ for a root of f. If f satisfies certain assumptions and the initial guess is close, then x₁ = x₀ - f(x₀)/f'(

Newton-Raphson Method for Nonlinear Systems of Equations

mathswithmuza on Instagram: "Newton–Raphson is an iterative method for finding solutions to equations of the form f(x) = 0. Instead of trying to solve the equation directly, it starts with an initial guess and improves that guess step by step. The key idea is to use the tangent line at the current point as a local approximation of the curve. If you know the value of the function and its derivative at a point, you can follow the tangent line down to where it crosses the x-axis. That crossing beco