Ch 62: MTEL Math: Graphing Derivatives & L'Hopital's Rule

About This Chapter

In this chapter, you will review the processes of graphing derivatives from functions and using differentiation to find the maximum and minimum values of a graph. Use these lessons to prepare for related questions on the MTEL Mathematics exam.

MTEL Math: Graphing Derivatives & L'Hopital's Rule - Chapter Summary

Follow along with our expert instructors in this series of short, engaging lesson videos to prepare for questions on the Massachusetts Tests for Educator Licensure (MTEL) Mathematics exam about the different procedures used to graph derivatives, data mine and use L'Hopital's Rule. In these lessons, our professional instructors will demonstrate these procedures so that you can follow along and improve your own skills. After these lessons, you should possess an improved ability to:

  • Graphing derivatives from functions
  • Understanding non-differentiable derivatives graphs
  • Finding minimum and maximum graph values
  • Understand the use of differentiation
  • Identifying a graph's concavity and inflection points
  • Data mining: finding function properties from derivatives
  • Identifying functions from derivative graphs
  • Defining and applying L'Hopital's rule in complex and simple instances

After watching these videos, reinforce your retention of the material presented in them by reading the transcripts. Then, take the lesson quizzes to discover topics you don't understand. To improve your understanding of the topics, use the video tags to return to and review the parts of the lessons.

MTEL Math: Graphing Derivatives & L'Hopital's Rule Objectives

The MTEL Mathematics exam is a certification exam used by the state of Massachusetts to test the competency of future math teachers. When you take this computer-based exam, you will be asked to complete 100 multiple-choice questions and two open-response assignments in a four-hour testing session. Sixteen percent of the material covered in this exam will be multiple-choice questions about topics of trigonometry, calculus and discrete mathematics. Use this chapter to prepare for some of the questions in this domain that will ask you about derivatives and differential calculus.

11 Lessons in Chapter 62: MTEL Math: Graphing Derivatives & L'Hopital's Rule
Test your knowledge with a 30-question chapter practice test
Graphing the Derivative from Any Function

1. 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!

Non Differentiable Graphs of Derivatives

2. Non Differentiable Graphs of Derivatives

When I walk along a curve, I stand normal to it. That is, I stand perpendicular to the tangent. Learn how to calculate where I'm standing in this lesson.

How to Determine Maximum and Minimum Values of a Graph

3. 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.

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.

Concavity and Inflection Points on Graphs

5. 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.

Understanding Concavity and Inflection Points with Differentiation

6. 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.

Data Mining:  Function Properties from Derivatives

7. Data Mining: Function Properties from Derivatives

Some shoes come with accelerometers that give a person's acceleration as a function of time. From this information, the shoe can determine roughly how fast you're going. In this lesson, learn how this works as we take the derivative of a function and glean information from it about the original function.

Data Mining:  Identifying Functions From Derivative Graphs

8. Data Mining: Identifying Functions From Derivative Graphs

If you saw the graph of speed as a function of time for a bicycle, a jet, and a VW bug, could you pick which vehicle produced which graph? In this lesson, try it as we match functions with their derivatives.

What is L'Hopital's Rule?

9. What is L'Hopital's Rule?

A Swiss mathematician and a French mathematician walk into a bar ... and they walk out with the famous L'Hopital's rule for finding limits. In this lesson, learn what these two mathematicians came up with and how to use it to avoid the limit of zero divided by zero!

Applying L'Hopital's Rule in Simple Cases

10. Applying L'Hopital's Rule in Simple Cases

L'Hôpital's rule may have disputed origins, but in this lesson you will use it for finding the limits of a range of functions, from trigonometric to polynomials and for limits of infinity/infinity and 0/0.

Applying L'Hopital's Rule in Complex Cases

11. Applying L'Hopital's Rule in Complex Cases

L'Hôpital's rule is great for finding limits, but what happens when you end up with exactly what you started with? Find out how to use L'Hôpital's rule in this and other advanced situations in this lesson.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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