Daily Prep 8A -- MTH 201-04

--- tags: mth201, dailyprep --- # Daily Prep 8A -- MTH 201-04 ## Overview Module 8 is a continuation of the concepts of Module 7 where we analyzed the behavior of a function by finding and classifying its critical values and examining its concavity; it's also an important setup for Module 9, where we look at applied problems involving finding the "best" values of a function. In Module 8A we introduce the **Extreme Value Theorem**, which states that every continuous function has an absolute/global maximum and minimum function if it's constrained to a closed interval. This mathematical result gives us a simplified process for finding global max and min values of functions. ## 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*) Find the critical values of a function using its first derivative, and classify them using the First or Second Derivative Tests. + (*Review*) State the definition of a **closed interval**. + (*Review*) State informally what it means for a function to be **continuous on a closed interval**. + 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. + Apply the Extreme Value Theorem to find the absolute maximum and minimum values of a continuous function on a closed interval. + 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 3.3](https://activecalculus.org/single/sec-3-3-optimization.html). **Video:** Watch the following from the GVSUMath Calculus playlist. - Screencast 3.3.1: Quick review -- Global optimization (2:31) https://www.youtube.com/watch?v=ldJfxeGHv3Y&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=66 - Screencast 3.3.2: Finding absolute extreme values (8:08) https://www.youtube.com/watch?v=YE57SJzL8r8&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=67 - Screencast 3.3.3: Optimizing population (7:09) https://www.youtube.com/watch?v=kz9JFNlQVVI&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=68 ## Exercises The exercises for this Daily Prep are found on student.desmos.com. ## Submission and grading To submit your work, simply do the work in 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.