#math/calculus ![[Pasted image 20260927182615.png]] Newton’s method is a way to find where a function crosses the \(x\)-axis, meaning where f(x)=0. You start with a guess \(x_0\) near the root. At \(x_0\), draw the tangent line to the curve. That tangent line will usually cross the \(x\)-axis closer to the true root. Call that new point \(x_1\). The formula above computes where the tanglent line at $x_{n}$ hits the $x\text{-axis}$ $ y=f(x_{n})+f'(x_{n})(x-x_{n}) $ ^[remember $x_{n}$ is just acting as a displacement to wherever $x_{n}$ is, kinda like making it the origin.] Insert image of example of one iteration of newton method. Show what each $f(x_{n})$, $f'(x_{n})$, $x,x_{n}$ are. Then show after iteration lets say 10, it means $f(\bar{x})=0$.