Introduction to Derivatives

Introduction

A Webquest for 11th-12th Graders (Calculus)

Designed by

Tim Dignan

Introduction: You are a student getting prepared for your first calculus test on derivatives. The problem is you don’t quite understand where a derivative comes from or what it represents and you frequently think to yourself “what in the world am I finding right now and what does it mean?” This Webquest will help students better understand what in the world a derivative is and how to find the derivative from the definition of derivatives.

Task

Task: Your Job is to learn how to find the derivative of a function efficiently using the definition of the derivative limit process. You must then be able to state what you have found and what it represents in regards to the function. It is also important for you to think of an application for the derivative. This will help students appreciate finding the derivative more by realizing what the purpose of finding a derivative is.

Process

Process: Step One- In order to find the derivative you must first know and understand the definition of the derivative. There are many shortcuts to finding derivatives but it is important to first understand how to find the derivative using the limit process. This will help to better understand where the derivative comes from. This website shows the definition of the derivative and should help you be able to then find the derivative using the given limit process.

Definition of Derivative

Step 2- After reading and looking at some examples using the limit process of the definition of derivatives you will find the derivative of the following function using the information you learned from step one. The function is listed below.

F(x)= 5x^3-5
To check yourself to make sure you have gotten the right final answer use this derivative calculator link given below to see if your answer matches.

Derivative Calculator

Step 3- After solving the derivative it’s important for you to understand what the significance of the solution that you acquired. State what the derivative represents in regards to the original function and a potential application the derivative could be used. This website below gives a good explanation on what the derivative represents and how they are applied.

Derivative Representation/Application

Evaluation

Evaluation: Score


	Beginning 1	Developing 2	Accomplished 3	Exemplary 4
Derivative Was Found Using Limit Process.	No Answer was found for the derivative.	Answer was found but with little or no work.	Answer was found but not found by complete use of limit process.	Answer was found by complete use of the limit process.
State What Derivative Represents in Regards to the Original Function.	No representation was given.	Representation was given but was incorrect.	Representation was given with some correct point but not completely correct.	Representation was given with complete and correct definition.
State a Potential Application the Derivative Found Could be Used For.	No Application was given.	Application was given but was an incorrect use.	Application was given with some correct points but not completely correct.	Application was given with complete and correct application.

Conclusion

Conclusion: Now that you have completed the given tasks, you have learned how to find the derivative using the limit process from the definition of derivatives. You also know what the derivative represents in regards to the original function and a potential application the derivative could be used for. You will move on to learn some shortcuts that make finding derivatives easier so the limit process will not be necessary. Here is a link below showing some of the shortcuts used to find derivatives.

Derivative Shortcuts

Credits

Credits:

Introduction to Derivatives Pictures:

http://bealingmath.wikispaces.com/Curve+Sketching

https://play.google.com/store/apps/details?id=com.andymc.derivative

Step One Link:

http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfDerivative.aspx

Step Two Link:

http://www.derivative-calculator.net/#

Step Three Link:

http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/derivs/deriv5.html

Conclusion Link:

http://www.empirenet.com/tajames/calculus/notes-derivative-shortcuts.html

Teacher Page

I created this page to help students understand how derivatives work and why they are used. I am an Integrated Mathematics Major at Ohio University and plan to become a high school mathematics teacher. Hope you enjoy!

Tim Dignan