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Ch 4: Calculating & Graphing Derivatives in Business Calculus Lesson Plans

About This Chapter

The Calculating & Graphing Derivatives in Business Calculus chapter of this course is designed to help you plan and teach derivative calculations in your classroom. The video lessons, quizzes and transcripts can easily be adapted to provide your lesson plans with engaging and dynamic educational content. Make planning your course easier by using our syllabus as a guide.

Weekly Syllabus

Below is a sample breakdown of the Calculating & Graphing Derivatives in Business Calculus chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.

Day Topics Key Terms and Concepts Covered
Monday Derivatives of complex functions Using the chain rule to differentiate nested equations, trig functions and exponential functions
Tuesday Higher order derivatives Finding second, third and fourth order derivatives; understanding graphs of higher order derivatives
Wednesday Maximum and minimum values Finding a function's extrema; determining minimum and maximum values of a graph
Thursday Concavity and inflection points Relating derivatives to a function's concavity and inflection points
Friday Curve sketching Determining a graph's concavity and inflection points, intercepts and asymptotes

8 Lessons in Chapter 4: Calculating & Graphing Derivatives in Business Calculus Lesson Plans
Test your knowledge with a 30-question chapter practice test
Using the Chain Rule to Differentiate Complex Functions

1. Using the Chain Rule to Differentiate Complex Functions

If you've ever seen a complicated function, this lesson is for you. Most functions that we want to differentiate are complicated functions, for which no single derivative rule will work. In this lesson, learn how to use the chain rule to simplify nesting equations.

Calculating Higher Order Derivatives

2. Calculating Higher Order Derivatives

Differentiating functions doesn't have to stop with the first or even second derivative. Learn what a mathematical jerk is as you calculate derivatives of any order in this lesson.

Understanding Higher Order Derivatives Using Graphs

3. Understanding Higher Order Derivatives Using Graphs

The derivative is a rate of change, like velocity. What happens, though, when your velocity - that is, your rate of change - is changing? Explore the changing changes in this lesson.

Using Differentiation to Find Maximum and Minimum Values

4. Using Differentiation to Find Maximum and Minimum Values

If you are shot out of a cannon, how do you know when you've reached your maximum height? When walking through a valley, how do you know when you are at the bottom? In this lesson, use the properties of the derivative to find the maxima and minima of a function.

Understanding Concavity and Inflection Points with Differentiation

5. Understanding Concavity and Inflection Points with Differentiation

Put a little more meaning behind those cups and frowns. In this lesson, use the second derivative of a function to determine if it is concave up or concave down.

Concavity and Inflection Points on Graphs

6. Concavity and Inflection Points on Graphs

You might not think of a cup when you think of an awesome skateboard ramp. But I'm sure a really bad ramp would give you a frown, right? Learn about cups and frowns in this lesson on concavity and inflection points.

Curve Sketching Derivatives, Intercepts & Asymptotes

7. Curve Sketching Derivatives, Intercepts & Asymptotes

This lesson presents a calculus-based procedure for graphing various types of functions. The methods used will be based on using derivatives, intercepts, and asymptotes for graphing functions.

How to Determine Maximum and Minimum Values of a Graph

8. How to Determine Maximum and Minimum Values of a Graph

What is the highest point on a roller coaster? Most roller coasters have a lot of peaks, but only one is really the highest. In this lesson, learn the difference between the little bumps and the mother of all peaks on your favorite ride.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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