Optimization is the process of discovering the [[Critical Points]] of a [[Function]]. The most common way to aproach this problem is to find the extrema of a [[Function]] $f$ with respect to $x$, we find the [[Roots]] of its [[Derivative]] $\deriv{f}{x}$. >[!info] >![[Roots Problem into Fixed Point Problem]] We can use the following to make this iterative method to find the [[Critical Points]] of $f$. $\huge \begin{align} x_{i+1} &= x_{i} + \gamma f'(x_{i}) \end{align} $ Note $\gamma\in \R$ and if positive then this method will convergence to a [[Maxima]] of $f$, while negative $\gamma$ will convergence to a [[Minima]] of $f$.