Newton's method in optimization

In calculus, Newton's method (also called Newton–Raphson) is an iterative method for finding the roots of a differentiable function ${\displaystyle f}$, which are solutions to the equation ${\displaystyle f(x)=0}$. However, to optimize a twice-differentiable ${\displaystyle f}$, our goal is to find the roots of ${\displaystyle f'}$. We can therefore use Newton's method on its derivative ${\displaystyle f'}$ to find solutions to ${\displaystyle f'(x)=0}$, also known as the critical points of ${\displaystyle f}$. These solutions may be minima, maxima, or saddle points; see section "Several variables" in Critical point (mathematics) and also section "Geometric interpretation" in this article. This is relevant in optimization, which aims to find (global) minima of the function ${\displaystyle f}$.