---
tags: mth201, dailyprep
---

# Daily Prep 7B -- MTH 201-04

## Overview

In this module we extend the idea of the First Derivative Test from Module 7A to accomplish the same thing but using the second derivative instead. When the second derivative of a function can be calculated easily, it gives us a simpler way to classify critical numbers as local extrema --- using a procedure known as the **Second Derivative Test**. While we're thinking about second derivatives, in Module 7B we'll also learn about using the second derivative to pinpoint concavity behavior of a function's graph.

## 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.

+ (*Review*) Identify where a function is concave up or concave down by examining its graph.
+ (*Review*) Given information about the sign of the second derivative of a function at a point, state whether the function is concave up or concave down at that point.

**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.

+ Use the Second Derivative Test to determine whether a critical number of a function is a relative minimum or relative maximum.
+ Use the second derivative of a function to determine its intervals of concavity and inflection points.

## Resources for learning

**Reading:** In the _Active Calculus_ text, read in [Section 3.1](https://activecalculus.org/single/sec-3-1-tests.html) starting with Example 3.1.10 and continuing through the end. There is a video walkthrough for Example 3.1.10 that you should watch either just before or just after reading that example.

**Video:** First watch these from the GVSUMath Calculus playlist:

- Screencast 3.1.6: The Second Derivative Test (8:53) https://www.youtube.com/watch?v=4Z_lhNVXEV4&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=60
- Screencast 3.1.7: Identifying inflection points graphically (7:03) https://www.youtube.com/watch?v=Tyyo8kILvE0&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=61
- Screencast 3.1.8: Finding inflection points (7:31) https://www.youtube.com/watch?v=w_O9IKmDZMI&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=62

THEN, watch this video which is a walkthrough of Example 3.1.10 in the reading:

https://gvsu.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=544276df-e3ea-484b-9868-ac4f00ce94fd

This is also embedded on Blackboard in the *Module 7* folder.

## Exercises

The exercises for this Daily Prep are NOT on Desmos but on this Google Form:

https://docs.google.com/forms/d/e/1FAIpQLSdAKNEFgybRcY-ZaZ_7VAlO8U5ictdqrLTU8PeOdC8txyJ1Yw/viewform

## Submission and grading

To submit your work, simply submit the Google Form. You will receive a receipt via email to confirm your submission. (Look in your spam folders if you do not see the receipt.)

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.