About This Chapter
Below is a sample breakdown of the Derivatives of Functions 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||Marginal analysis||Functions for marginal cost, revenue and profit; approximation formulas|
|Tuesday||Derivatives of implicit functions||Implicit functions, steps in implicit differentiation|
|Wednesday||Exponential functions||Definition of exponential functions and their graphs|
|Thursday||Derivatives of exponential functions||Derivative rules for exponential functions|
|Friday||Graphs of derivatives||Methods for finding continuous or discontinuous derivatives with a function's graph|
1. Implicit Functions
Sometimes inputting a variable into a function 'black box' doesn't yield a simple output. Find out what happens when you can't isolate the dependent variable on one side of the equal sign.
2. How to Find Derivatives of Implicit Functions
How do you define the rate of change when your function has variables that cannot be separated? Learn how implicit differentiation can be used to find dy/dx even when you don't have y=f(x)!
3. What Is an Exponential Function?
Brand new technologies don't always catch on right away because they can be expensive and don't always work as well as they should. But once the price comes down, and they start to work better, it doesn't take very long before it seems like everyone has one. Learn about the numbers behind this, exponential functions!
4. Calculating Derivatives of Exponential Equations
Earth's population is booming! But why is the population increasing so much more drastically than it did many years ago? In this lesson, learn how to calculate the rates of change in exponentials by discovering the rules of derivatives with exponents.
5. Graphing the Derivative from Any Function
When you know the rules, calculating the derivates of equations is relatively straightforward, although it can be tedious! What happens, though, when you don't know the function? In this lesson, learn how to graph the derivative of a function based solely on a graph of the function!
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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
- Calculating & Graphing Derivatives 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