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 ┬áin 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.
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