About This Chapter
Below is a sample breakdown of the Graphing Derivatives and L'Hopital's Rule 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||Graphing the Derivative of a Function||Directions for graphing the derivative of a given function, such as location; equation of a normal line and non-differentiable graphs of derivatives|
|Tuesday||Maximum and Minimum Values on a Graph||Instructions for finding maximum and minimum points or values on graphs, including the definition of extrema and use of differentiation|
|Wednesday||Concavity and Inflection Points on Graphs||Graphical definitions of concave down and concave down, including the use of the second derivative of a function to make the determination|
|Thursday||Data Mining: Derivatives of Functions and Their Properties||Relationship between the derivative of a function and the properties of the original function; matching functions with graphs of derivatives with their original functions|
|Friday||L'Hopital's Rule: Definition and Applications||Description of L'Hopital's Rule and its use in calculating limits; applying the rule in basic and complex cases|
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!
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.
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.
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.
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.
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.
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.
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.
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!
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.
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.
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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
- Applications of Derivatives: 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