About This Chapter
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|
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.
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.
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.
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.
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.
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.
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.
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.
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Other chapters within the Business Calculus Syllabus & Lesson Plans course
- Functions for Business Calculus Lesson Plans
- Working with Limits in Business Calculus Lesson Plans
- Derivatives & Differentiation in Business Calculus Lesson Plans
- Derivatives of Functions in Business Calculus Lesson Plans
- Optimization in Business Calculus Lesson Plans
- Logarithms in Business Calculus Lesson Plans
- Integrals in Business Calculus Lesson Plans
- Growth Models in Business Calculus Lesson Plans
- Multi-Variable Calculus Lesson Plans