Module 3: The Derivative (Chapter 2, cont.)

The Hennessey Venom GT is one of the fastest cars in the world. In 2014, it reached a record-setting speed of 270.49 mph. It can go from 0 to 200 mph in 14.51 seconds. The techniques in this chapter can be used to calculate the acceleration the Venom achieves in this feat (see "Chapter Opener: Estimating Rate of Change of Velocity" Example in Section 2.2: The Derivatives).

Calculating velocity and changes in velocity are important uses of calculus, but it is far more widespread than that. Calculus is important in all branches of mathematics, science, and engineering, and it is critical to analysis in business and health as well. 

In this chapter, we explore one of the main tools of calculus, the derivative, and show convenient ways to calculate derivatives. We apply these rules to a variety of functions in this chapter so that we can then explore applications of these techniques.

Image Caption: The Hennessey Venom GT can go from 0 to 200 mph in 14.51 seconds. (credit: modification of work by Codex41, Flickr)

(Content & Image Source: Chapter 3 Introduction, Calculus Volume 1, Gilbert Strang and Edwin "Jed" Herman, OpenStax, CC BY-NC-SA License)

• Define velocity as a rate of change
• Calculate the average rate of change of a function, distinguish it from the instantaneous rate of change, and explain their relationships with secant and tangent lines.
• Describe the derivative as the limit of a difference quotient and the slope of the tangent line to the graph of the function at the point.
• Calculate the derivative of a given function at a specific point using limits.

• State the constant, constant multiple, and power rules.
• Apply the sum and difference rules to combine derivatives.
• Compute the derivative of e^x
• Find equations of tangent lines
• Solve applications with the derivative

• Use the Product and Quotient Rules to find derivatives
• Solve applications with the derivative

• Use the Chain Rule to find derivatives
• Solve applications with the derivative
• Describe the relationship between differentiable and continuity

1. Read the Module 3 Introduction (see above).
   
2. Read Sections 2.2 - 2.5 of Chapter 2: Limits and The Derivative in Applied Calculus (links to each Section provided below)
   • At the end of this Section there is a list of Vocabulary, a Self Check Quiz, and a set of Flashcards
     
3. Watch the Videos for each Section (links provided below)
   
4. Complete the MyOpenMath Homework Assignments for each Section (links provided below) - These are graded!
   
5. Practice the problems on the Chapter 2 Review Exercises - The Derivative, checking the solutions provided (link provided below)
6. Complete the MyOpenMath Quizzes for Chapter 2 (link provided below) - These are graded!
7. Once you complete the Quizzes, upload your work in the Quiz Work Upload Assignment using the submission link below.
8. Post in the Chapter 2 Q&A Discussion Forum - link provided below.
   

Module Pressbooks Resources and Activities