About This Chapter
Below is a sample breakdown of the Applications of Derivatives 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|| Linearization of Functions; |
How to Estimate Function Values Using Linearization
| Determine travel times and distances by using the process of linearization; |
Using linearization to determine velocity
|Tuesday|| What is Newton's Method?; |
How to Use Newton's Method to Find Roots of Equations
| An explanation of Newton's Method and linearization; |
The steps necessary for solving equations with this method
|Wednesday||Optimization and Differentiation||The five steps for solving optimization problems|
|Thursday||Optimizing Simple Systems||A formula for solving optimization problems|
|Friday||Optimizing Complex Systems||The rules for solving more complex optimization equations|
1. Linearization of Functions
Over the river and through the woods to Grandmother's house we go ... Are we there yet? In this lesson, apply linearization to estimate when we will finally get to Grandma's house!
2. How to Estimate Function Values Using Linearization
Sometimes landing on Mars isn't that easy. You might need to use linearization to estimate if you will crash into the planet, or miss it entirely. Learn how to do just that in this lesson.
3. What is Newton's Method?
Hang gliding can be perilous, especially if you think you might land in a stinky pigpen. In this lesson, find out how Newton's Method might help you determine whether you'll be covered in mud when you land.
4. How to Use Newton's Method to Find Roots of Equations
Finding the roots of equations usually requires the use of a calculator. However, in this lesson you'll use Newton's Method to find the root of any equation, even when you can't solve for it explicitly.
5. Optimization and Differentiation
In this lesson, you can learn what optimization means from a mathematical standpoint. Using the techniques taught in this lesson, you can use the five steps to optimization to figure out practical things, like how much sleep you need to get before an exam.
6. Optimizing Simple Systems
Optimization problems may seem overwhelming, but they can actually be quite simple. In this lesson, learn how to use a handy five-step formula to tackle these daunting problems.
7. Optimizing Complex Systems
In this lesson, you'll learn how to follow a five-step process to solve complex optimization problems by visualizing, defining, writing an equation, finding the minimum or maximum, and answering the question.
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Other chapters within the Calculus Syllabus Resource & Lesson Plans course
- Graphing & Functions: Calculus Lesson Plans
- Continuity: Calculus Lesson Plans
- Geometry & Trigonometry: Calculus Lesson Plans
- Using Scientific Calculators: Calculus Lesson Plans
- Limits: Calculus Lesson Plans
- Rate of Change: Calculus Lesson Plans
- Calculating Derivatives: Calculus Lesson Plans
- Derivative Graphs & L'Hopital's Rule: Calculus Lesson Plans
- Area Under the Curve & Integrals: Calculus Lesson Plans
- Integration: Calculus Lesson Plans
- Integration Applications: Calculus Lesson Plans
- Differential Equations: Calculus Lesson Plans