What is Newton's method in optimization?

In calculus, Newton's method is an iterative method for finding the roots of a differentiable function F, which are solutions to the equation F = 0. As such, Newton's method can be applied to the derivative f ′ of a twice-differentiable function f to find the roots of the derivative = 0], also known as the critical points of f. These solutions may be minima, maxima, or saddle points; see section "Several variables" in Critical point and also section "Geometric interpretation" in this article. This is relevant in optimization, which aims to find minima of the function f.