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First Derivative Test Worksheet – Calculus Extrema Practice
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Description
What It Is:
A calculus worksheet designed to help students apply the First Derivative Test to identify relative maxima and minima of polynomial functions. Exercises include differentiating, finding critical points, and analyzing sign charts to determine where functions increase or decrease.
Why Use It:
Builds confidence in using derivatives to analyze function behavior. Strengthens understanding of how to use the First Derivative Test for classifying extrema and understanding slope changes on graphs.
How to Use It:
• Differentiate each function to find f′(x).
• Set f′(x) = 0 and solve for critical points.
• Use a sign chart to determine where f′(x) changes sign.
• Identify relative maxima, minima, or points of inflection.
• Optional: Sketch graphs to visualize increasing/decreasing intervals.
Grade Suitability:
Best for Grades 11–12.
• Grade 11: Introduces the concept of slope and function analysis through derivatives.
• Grade 12: Reinforces calculus reasoning and prepares students for AP Calculus topics such as optimization and curve sketching.
Target Users:
Designed for Calculus and Precalculus teachers helping students master derivative-based problem solving, identify extrema, and analyze real-world graph behavior.
A calculus worksheet designed to help students apply the First Derivative Test to identify relative maxima and minima of polynomial functions. Exercises include differentiating, finding critical points, and analyzing sign charts to determine where functions increase or decrease.
Why Use It:
Builds confidence in using derivatives to analyze function behavior. Strengthens understanding of how to use the First Derivative Test for classifying extrema and understanding slope changes on graphs.
How to Use It:
• Differentiate each function to find f′(x).
• Set f′(x) = 0 and solve for critical points.
• Use a sign chart to determine where f′(x) changes sign.
• Identify relative maxima, minima, or points of inflection.
• Optional: Sketch graphs to visualize increasing/decreasing intervals.
Grade Suitability:
Best for Grades 11–12.
• Grade 11: Introduces the concept of slope and function analysis through derivatives.
• Grade 12: Reinforces calculus reasoning and prepares students for AP Calculus topics such as optimization and curve sketching.
Target Users:
Designed for Calculus and Precalculus teachers helping students master derivative-based problem solving, identify extrema, and analyze real-world graph behavior.
