About This Chapter
Who's It For?
Anyone who needs help learning or mastering AP calculus material will benefit from taking this course. There is no faster or easier way to learn AP calculus. Among those who would benefit are:
- Students who have fallen behind in understanding applications of derivatives
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about applications of derivatives
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How It Works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the applications of derivatives in AP calculus chapter exam.
Why it works:
- Study Efficiently: Skip what you know; review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the applications of derivatives in AP calculus chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any question on derivative applications. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
This chapter helps students review the concepts in an applications of derivatives unit of a standard AP Calculus AB and BC course. Topics covered include:
- Defining linearization of functions
- Estimating function values using linearization
- Finding roots of equations using Newton's method
- Comparing optimization and differentiation
- Optimizing complex systems
- Optimizing simple systems
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.
8. Chain Rule in Calculus: Formula & Examples
Learn how the chain rule in calculus is like a real chain where everything is linked together. Also learn what situations the chain rule can be used in to make your calculus work easier.
9. Taylor Polynomial: Formula & Examples
In this lesson we explore the Taylor polynomial, which serves as a way to approximate a given function near a given point. Two examples will be worked out in detail.
10. Taylor Series: Definition, Formula & Examples
In mathematics, we sometimes gain insights by expressing functions in different ways. One of those ways is the Taylor series. In this lesson, we will define the Taylor series and use examples to demonstrate its use.
11. How to Use the Second Derivative Test
In this lesson, we will learn what the second derivative test is and how to use it to analyze functions. We will examine the steps involved in using this test and then use it in a real world application.
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Other chapters within the AP Calculus AB & BC: Help and Review course
- Functions in AP Calculus: Help and Review
- Graphing and Functions in AP Calculus: Help and Review
- Sequences and Series in AP Calculus: Help and Review
- Limits in AP Calculus: Help and Review
- Continuity in AP Calculus: Help and Review
- Exponentials and Logarithms in AP Calculus: Help and Review
- Exponents and Polynomials in AP Calculus: Help and Review
- Calculating Derivatives & Derivative Rules in AP Calculus: Help & Review
- Calculus - Derivatives Calculations & Rules: Help & Review
- Differential Equations in AP Calculus: Help and Review
- Area Under the Curve and Integrals in AP Calculus: Help and Review
- L'Hopital's Rule & Graphing Derivatives: Help & Review
- Integration Applications in AP Calculus: Help and Review
- Rate of Change in AP Calculus: Help and Review
- Geometry and Trigonometry in AP Calculus: Help and Review
- How to Use Scientific Calculators for AP Calculus: Help and Review