Newton's Method is a second-order optimization algorithm that relies on the second-order Taylor expansion of a multivariate function $f(\mathbf{x})$. By taking the expansion $f(\mathbf{x} + \boldsymbol{\epsilon}) = f(\mathbf{x}) + \boldsymbol{\epsilon}^ op abla f(\mathbf{x}) + \frac{1}{2} \boldsymbol{\epsilon}^ op \mathbf{H} \boldsymbol{\epsilon} + \mathcal{O}(\|\boldsymbol{\epsilon}\|^3)$, where $\mathbf{H} = abla^2 f(\mathbf{x})$ is the Hessian matrix, and setting the derivative with respect to the update step $\boldsymbol{\epsilon}$ to zero ($abla f(\mathbf{x}) + \mathbf{H} \boldsymbol{\epsilon} = 0$), the algorithm derives the optimal update step as $\boldsymbol{\epsilon} = -\mathbf{H}^{-1} abla f(\mathbf{x})$. This approach requires computing and inverting the Hessian matrix to directly jump toward the function's minimum.