Calculus · Week 20 · Analytical Applications of Differentiation
Concavity and the Second Derivative
Concavity, points of inflection, and seeing a classmate's method as another valid view.
- Students will
- Students find f''(x), state where f is concave up or down, find a point of inflection, and apply the second derivative test.
- SEL skill
- Explain how a partner's method sees the same point before judging which method fits
- What it looks like
- Students practice social awareness by explaining how a classmate's method, the first derivative test, reaches the same or a different conclusion.
- Content focus
- Concavity and the second derivative test
- Format
- Structured discussion
Social awareness
Social awareness means understanding how other people see things, like following how a classmate's method reaches a conclusion about a curve. More social awareness activities
What you get
A teacher guide with what to say, step by step, plus student pages and a supports page for students with diverse learning needs, including those with IEPs. Print or Project it, or assign it in Google Forms and Google Docs for Google Classroom. Your first 10 activities are free.
Standards
- AB 5.6: AP Calculus AB, Unit 5, Topic 5.6
- AB 5.7: AP Calculus AB, Unit 5, Topic 5.7
- Standard for Mathematical Practice: MP3 Construct viable arguments and critique the reasoning of others
- CA Mathematics Framework (2023): Exploring Changing Quantities
- Traditional course: Calculus
More social awareness activities for Calculus
- Squeeze and Infinity Social awarenessThe squeeze theorem, infinite limits, and limits at infinity, comparing a classmate's method with your own.
- Smooth or Sharp? Differentiability Social awarenessEstimating derivatives and seeing where a graph is smooth, cornered, or too steep, by looking from both sides.
- Motion: Position, Velocity, Acceleration Social awarenessReading the signs of velocity and acceleration to tell a motion story.
- The Fundamental Theorem of Calculus Social awarenessThe Fundamental Theorem links derivatives and integrals; seeing a classmate's reasoning from their side.
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RoseThread Connect activities are drafted with the help of AI and shaped by educators. Students never have to share anything personal. Our five SEL skills are informed by CASEL's SEL Framework; RoseThread Learning is not affiliated with or endorsed by CASEL. AP and Advanced Placement are trademarks of the College Board, which was not involved in making and does not endorse RoseThread Connect.