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Unit B Concepts 1-2: Finding Extrema and Intervals of Increase and Decrease

Unit B Concepts 1-2: Finding Extrema and Intervals of Increase and Decrease

Author: Crystal Kirch

Finding relative minimum and relative maximum values of a polynomial with a graphing calculator

Identifying intervals of increase and decrease of a polynomial

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Do you ever have ups and downs?

I think we all do... and graphs do, too!

I bet you never knew that graphs had mood swings.  We call those mood swings intervals of increase (good moods) and intervals of decrease (bad moods).  There are also very high points (maximum values) and very lllllloooooooowwwwwwwww points (minimum values).

In this tutorial, we will learn how our graphing calculator helps us to find those values accurately.  Yes, a graphing calculator is required for this tutorial! (Hopefully you followed the instructions on the letter and talked with us before summer break if this was a problem!)  If for some reason you don't have a graphing calculator yet, you can move on to the next tutorial and come back to this one when you are ready.

​This tutorial is really all about getting to know the graphing calculator and doing a lot of "button-pushing" - but, you will be using these skills for the entire school year, so it is VITAL that you commit these processes to memory and know how to find them automatically without having to look at the steps.



To remind you:

Even though you may be saying, "Oh yeah, I got this"... PLEASE PLEASE PLEASE make sure to FULLY understand the details of this concept. It's MORE than just solving the problems in Math Analysis...

YOU MUST BE ABLE TO SOLVE, EXPLAIN YOUR THOUGHT PROCESSES, AND MAKE CONNECTIONS among these concepts - it's more than just rote memorization!

Start yourself on the right path by taking even these "beginning concepts" seriously!


This video will review what Unit B is all about and teach you how to find relative maximums and minimums on your graphing calculator.

If you do not yet have one, CONTACT MRS. KIRCH IMMEDIATELY!

You can move on to concept 3 and continue through Unit D, coming back to these two concepts when you have your graphing calculator.

Source: Created by Crystal Kirch using Camtasia for Mac

Graphing Calculator Intro Video?

In the video above, I mention an intro sorry, but I don't have it made yet!  Please ask me for specific questions via email and I will reply as soon as I can.  If I get a chance to make it this summer, I will upload it here in this place.  thanks!


This video will show another example of how to use your graphing calculator to find extrema.

Source: Created by Crystal Kirch using Camtasia for Mac


This video will teach you what intervals of increase and decrease are, and how to identify them on a graph. There are some very important things to remember about writing intervals, such as the fact that they are all "open" intervals and that, although it's easiest to start by writing them in order from left to right, they must be split into intervals of increase and intervals of decrease when you write your answer.

Source: Created by Crystal Kirch using Camtasia for Mac

UNIT B CONCEPT 2 - PART 2 (optional)

This video will go over another example of writing intervals of increase and decrease for those of you who need to see it another time through.

Source: Created by Crystal Kirch using Camtasia for Mac

SSS Requirements

Before moving on, please make sure the following problems from your SSS are complete and correct, as based on what I went over in the video.


Page 2 #1-3

Page 3 #1,3, (4 is optional from Part 2 video)


Practice Quiz (PQ) requirements



Before moving on, please complete the following PQ problems on your own.

  • These problems must be done on lined paper and labeled clearly with “Unit ___ Concept ___ Practice Quiz” at the top of each page. PLEASE HIGHLIGHT THIS TITLE SO IT IS VERY CLEAR WHERE ONE ASSIGNMENT STARTS AND ENDS.
  • You must show all work, all steps, and all thought processes for these assignments. If you feel like you don’t need to show any work, you must explain your thought process in a few sentences. No step by step work = no credit.
  • You must check your answers to the PQ problems (answers are on the last page of each SSS packet) and re-work through any problems you got wrong.

You must MASTER this material, so if you are getting them wrong, you need to figure out how to do them correctly. Please contact me if you have a question (you can add a question at the end of this tutorial) and I can work out another example video for you.


​PQ 1 #1-2 (#3-4 suggested extra practice)

​PQ 2 #5-7 (#8 suggested extra practice)

Unit B Reflection (Concepts 1-2)

Please answer questions posed below correctly and completely.
You MUST re-watch the video if you don't know the correct answer.
Completely means:
1) Complete sentences
2) Detailed answers

Source: Created by Google Docs