---
# System prepended metadata

title: Daily Prep 9A -- MTH 201-04
tags: [' dailyprep', mth201]

---

---
tags: mth201, dailyprep
---

# Daily Prep 9A -- MTH 201-04

## Overview 

Module 9 focuses on an important class of problems that calculus answers well, called **applied optimization** problems. These take various forms but all ask *What is the "best" value of a function that has to satisfy constraints?* For example we might want to find the maximum volume of a box if we only have a certain amount of materials present to make it; or the lowest value of the cost of producing a new product when our advertising budget is constrained. Applied optimization is the clearest application of calculus there is, and it's both the culmination of everything we've learned about derivatives and the last module we will learn about derivatives. 

## 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*) State the **Extreme Value Theorem** and explain the three-step process it provides for finding the absolute extreme values of a continuous function on a closed interval. 

**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. 

+ Given an applied setting, build a function that models the situation; identify a closed interval for its domain; then identify its absolute maximum and minimum values on the interval. 


## Resources for learning

**Reading:** In the _Active Calculus_ text, read [Section 3.4](https://activecalculus.org/single/sec-3-4-applied-opt.html). 

**Video:** Watch the following videos from the GVSU Calculus playlist: 

- Screencast 3.4.1: Quick review -- Applied optimization (2:51) https://www.youtube.com/watch?v=Ilu2SZa3SYA&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=69
- Screencast 3.4.2: Fencing optimization (7:09) https://www.youtube.com/watch?v=jH6J-n6zt4c&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=70&t=7s
- Screencast 3.4.3: Optimization with trigonometry (13:25) https://www.youtube.com/watch?v=uJFxdxSBjok&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=71

**Other:** In addition to these from the GVSUMath playlist, there is an insane number of videos on YouTube from other sources that give examples of applied optimization problems. Just do a query under "applied optimization calclus". 

## Exercises 

The exercises for this Daily Prep are found on student.desmos.com. Look for "MTH 201 Daily Prep 9A".


## Submission and grading 

To submit your work, just do the work on Desmos. 

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.