## Tangent Lines, Velocities, and Growth

Read this section for an introduction to connecting derivatives to quantities we can see in the real world. Work through practice problems 1-4.

### Introduction

We estimated the slope of a line tangent to the graph of a function at a point and constructed a new function which was the slope of the line tangent to the graph of a function at each point. In both cases, before we could calculate a slope, we had to **estimate **the tangent line from the graph of the function, a method which required an accurate graph and good estimating. In this section, we will start to look at a more precise method of finding the slope of a tangent line which does not require a graph or any estimation by us. We will start with a nonapplied problem and then look at two applications of the same idea.

Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-2.1-Tangent-Lines-Velocities-Growth.pdf

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