---
tags: mth201, dailyprep
---

# Daily Prep 3A -- MTH 201-04

## Overview

Being able to compute derivatives is nice, but what's more important is **being able to interpret the information that those calculations give you**. (Most of the computations we've seen and will see can be done by a computer --- but computers can't interpret meaning!) This module looks at several important interpretive ideas that help us turn computations into information. In Part A, we'll look at how to estimate a derivative when you don't have much information about it, the information that the sign (positive/negative) of a derivative tells you about the derivative, and introduce the idea of the second derivative and concavity.

## Learning objectives

**Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught.

- If a function is given with units for the input and output, state the units of the derivative.
- Estimate the value of a derivative at a point using forward, backward, and central difference calculations.

**Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class.

- Determine whether a function is increasing, decreasing, or constant on an interval by examining the sign of its derivative. (Conversely, state the sign of a function's derivative using information about whether the function is increasing, decreasing, or constant.)
- Interpret the meaning of the derivative of a function that models a real-life situation, in terms instantaneous rates of change.

## Resources for learning

**Reading:** Read through [Section 1.5](https://activecalculus.org/single/sec-1-5-units.html) of the *Active Calculus* textbook. Work through the examples and all interactive exercises found at the end of the section.

**Video:** Watch the following videos and take notes.

- Screencast 1.5.1: Quick review: Interpreting, estimating, and using the derivative (3:27) http://www.youtube.com/watch?v=XZa0uNu6Uyk
- Screencast 1.5.2: Estimating the derivative (5:15) http://www.youtube.com/watch?v=wWdijnTdkTk

Also, watch at least one of the following videos, and as many as you find helpful. None of these were made at GVSU but have good explanations and examples about how to interpret the meaning of a derivative.

- Interpreting the meaning of a derivative in context (Khan Academy, 4:53) https://www.youtube.com/watch?v=IElkjzC9YhQ
- Interpreting the meaning of the derivative in context (Caculus AB/BC preparation, 5:49) https://www.youtube.com/watch?v=KRRVYYogYaA
- Interpretation of the derivative (CalculusSuccess, 12:00) https://www.youtube.com/watch?v=QirtTPD0Unk

For more such videos, do a YouTube search on "interpreting derivatives in context".

**Bonus screencast:** Estimating derivatives using spreadsheets (5:25) http://www.youtube.com/watch?v=CJ_OZ-Uxs3o&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=16 This isn't required, but if you know about (or are interested in learning about) spreadsheets, they can be a very handy tool in Calculus.

You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below.

## Exercises

The exercises for this Daily Prep are found on student.desmos.com.

## Submission and grading

To submit your work, simply do the work on Desmos. It will save as you go.

A **Pass** mark is given if the Daily Prep is turned in before its deadline and if each item on the Daily Prep has a response that represents a good faith effort to be right. **Mistakes are not penalized**. A **No Pass** is given if an item is left blank (even accidentally), has an answer but it shows insufficient effort (including responses like "I don't know"), or if the Daily Prep is late.