Calculus Second Derivative Test with Lesson Video (Unit 5)

Concavity & the Second Derivative Test Lesson:

Your AP Calculus students will find points of inflection and concavity of a function. Students will apply the Second Derivative Test to locate where concavity changes, extrema, and the behavior of a function. Your students will have guided notes, homework, and a content quiz on First Derivative Test - Increasing & Decreasing Functions that cover the concepts in depth from the six-lesson unit on Analytical Applications of Differentiation. #distancelearningtpt

What is included in this resource?

⭐ Guided Student Notes

⭐ Fully-editable SMART Board® Slides

⭐ Homework/Practice assignment

⭐ Content quiz

⭐ Video Lesson Link for Distance Learning - Flipped Classroom models

⭐ Full solution set

Lesson Objective:

★ Use the second derivative test to find points of inflection,. Intervals where the function is concave up or concave down, and to find maximum and minimum values.

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NOTE: This lesson has been updated to reflect the changes in the AP Calculus CED Binder and includes a LESSON VIDEO for Distance Learning needs.

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College Board® Topics:

Topic 5.6: Determining Concavity of Functions over Their Domains

Topic 5.7: Using the Second Derivative Test to Determine Extrema

College Board® Learning Objectives:

FUN-4.A: Justify conclusions about the behavior of a function based on the behavior of its derivatives.

FUN-4.A.4: The graph of a function is concave up (down) on an open interval if the function’s derivative is increasing (decreasing) on that interval.

FUN-4.A.5: The second derivative of a function provides information about the function and its graph, including intervals of upward or downward concavity.

FUN-4.A.6: The second derivative of a function may be used to locate points of inflection for the graph of the original function.

FUN-4.A.7: The second derivative of a function may determine whether a critical point is the location of a relative (local) maximum or minimum.

FUN-4.A.8: When a continuous function has only one critical point on an interval on its domain and the critical point corresponds to a relative (local) extremum of the function on the interval, then that critical point also corresponds to the absolute (global) extremum of the function on the interval.

The unit includes:

1) Mean Value Theorem

2) Extrema on an Interval

3) First Derivative Test

4) Second Derivative Test

5) Curve Sketching

6) Optimization

Click HERE to SAVE 20% by buying all ANALYTIC APPLICATIONS OF DIFFERENTIATION products, including cooperative activities, in UNIT 5 MEGA BUNDLE.

You might be interested in:

Applications of the Derivative Scavenger Hunt

Maximize-A-Box Optimization Project

Analytic Applications of Differentiation Unit Homework

Analytic Applications of Differentiation Assessments

Analytic Applications of Differentiation Essentials

Activities & Assessment Bundle

AP® is a registered trademark of the College Board® which was not involved in the creation of, and does not endorse this product.

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