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Ch 4: Calculating & Graphing Derivatives in Business Calculus

About This Chapter

The Calculating and Graphing Derivatives in Business Calculus chapter of this Business Calculus: Help and Review course is the simplest way to master calculating and graphing derivatives. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure you learn the essentials of calculating and graphing derivatives in business calculus.

Who's It For:

Anyone who needs help learning or mastering calculating and graphing derivatives material will benefit from the lessons in this chapter. There is no faster or easier way to learn calculating and graphing derivatives in business calculus. Among those who would benefit are:

  • Students who have fallen behind in understanding calculating and graphing derivatives in business calculus
  • Students who struggle with learning disabilities or learning differences, including autism and ADHD
  • Students who prefer multiple ways of learning business (visual or auditory)
  • Students who have missed class time and need to catch up
  • Students who need an efficient way to learn about calculating and graphing derivatives in business calculus
  • Students who struggle to understand their teachers
  • Students who attend schools without extra business 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 Calculating and Graphing Derivatives in Business 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 Calculating and Graphing Derivatives in Business Calculus chapter exam to be prepared.
  • Get Extra Support: Ask our subject-matter experts any question about calculating and graphing derivatives in business calculus. 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 a calculating and graphing derivatives unit of a standard business calculus course. Topics covered include:

  • Differentiating complex functions using the Chain Rule
  • Calculating and graphing higher order derivatives
  • Using differentiation to determine maximum and minimum values
  • Concavity and inflection points
  • Curve sketching
  • Minimum and maximum values of a graph

8 Lessons in Chapter 4: Calculating & Graphing Derivatives in Business Calculus
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.

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