Calculus · Week 19 · Analytical Applications of Differentiation
Finding Extreme Values
Critical points, sign charts, and choosing the right test to find local and absolute extreme values.
- Students will
- Students find critical points, build a sign chart for f', classify local extrema, and use the candidates test on a closed interval.
- SEL skill
- Choose the test that matches the question and give a reason before using it
- What it looks like
- Students practice responsible decision-making by choosing between the first derivative test and the candidates test and explaining the choice to the group.
- Content focus
- Critical points and extreme values
- Format
- Collaborative analysis
Responsible decision-making
Responsible decision-making means choosing a plan on purpose after weighing your options, like picking the test that matches what a calculus question asks. More responsible decision-making 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 5.3: AP Calculus AB, Unit 5, Topic 5.3
- AB 5.4: AP Calculus AB, Unit 5, Topic 5.4
- AB 5.5: AP Calculus AB, Unit 5, Topic 5.5
- Standard for Mathematical Practice: MP1 Make sense of problems and persevere in solving them
- CA Mathematics Framework (2023): Exploring Changing Quantities
- Traditional course: Calculus
More responsible decision-making activities for Calculus
- Continuity and the Intermediate Value Theorem Responsible decision-makingChecking continuity, fixing removable discontinuities, and deciding when the Intermediate Value Theorem applies.
- Inverse Functions and Their Derivatives Responsible decision-makingChoosing between the inverse derivative rule and inverse trig formulas, and explaining the choice.
- Choosing the Right Rule Responsible decision-makingReading how a function is built before choosing a derivative rule.
- Close Enough? Local Linear Approximation Responsible decision-makingUsing a tangent line to estimate and deciding whether to trust it.
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