## Optimization, Step 2

We’ll get really close to finding out why functions have minimums or maximums in this section. In order to do that, we’re going to need a few more tools. We’ll start with functions from $\mathbb R \rightarrow \mathbb R$, which are one dimensional in nature. Why are they one dimensional? The superscript on the first $\mathbb R$ is implicitly a $1$, i.e. $\mathbb R^1 \rightarrow \mathbb R^1$  in that we’re looking at functions of one independent variable. Soon we’ll generalize the results to $n$ dimensions, and eventually to infinitely many dimensions, but we have to start with one dimension.