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Ch 43: MTTC Math (Secondary): Graphing Derivatives & L'Hopital's Rule

About This Chapter

Add to what you've already learned about graphing derivatives and L'Hopital's rule when you watch the online video lessons in this chapter. Use the lessons to review the topics while you prepare to sit for the MTTC Math (Secondary) examination.

MTTC Math (Secondary): Graphing Derivatives and L'Hopital's Rule - Chapter Summary

Discover how much you remember about calculating derivatives and using L'Hopital's rule by watching these online video lessons. Expand your comprehension of extreme values and revisit the rules for determining the equation of a normal line. While preparing you for the MTTC Math (Secondary) examination, this chapter could help you with:

  • Graphing the derivative of functions
  • Understanding non-differentiable graphs as well as concavity and inflection points
  • Using differentiation and calculating a graph's maximum and minimum values
  • Identifying concave up and concave down
  • Describing the process of data mining
  • Defining and applying L'Hopital's rule

Instructors with years of mathematics experience present the material in these video lessons. Short and concise, the videos are thorough and allow for self-paced review. You could receive the benefit of the written transcripts, the clickable links for key terms and the self-assessment quizzes that follow all of the lessons.

MTTC Math (Secondary) Graphing Derivatives and L'Hopital's Rule Objectives

The MTTC Math (Secondary) examination is comprised of four sections. The Mathematical Processes and Number Concepts; Patterns, Algebraic Relationships and Functions; Measurement and Geometry; and Data Analysis, Statistics, Probability and Discrete Mathematics sections are equal to 22%, 28%, 22% and 28% of the examination score, respectively. When you demonstrate your understanding of derivatives and L'Hopital's rule on the examination, you could qualify for a mathematics teaching endorsement in Michigan.

There are two ways to take this examination: by paper or by computer. Teaching certification candidates who choose the paper-based examination have up to four hours and 30 minutes to answer 80 multiple-choice questions. Those who opt to take the computer-administered examination will have two hours and 30 minutes to answer the same number of multiple-choice questions.

11 Lessons in Chapter 43: MTTC Math (Secondary): 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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Other Chapters

Other chapters within the MTTC Mathematics (Secondary) (022): Practice & Study Guide course

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