11.1 Newton-Raphson Method

A kind of root finding algorithm

Equation of the straight line \[{}\] \[y - f(x_1) = f'(x_1)(x - x_1)\]

Intercept of x-axis \(x_2\) is when y = 0 \[{}\] \[\begin{align*} 0 - f(x_1) &= f'(x_1)(x_2 - x_1) \\ x_2 &= x_1 - \frac{f(x_1)}{f'(x_1)} \end{align*}\]

if we generalize this; \[{}\] \[x_{k+1} = x_k - \frac{f(x_k)}{f'(x_k)}\]