calculus 12 Applications of derivatives
Specific Curriculum Outcomes
B15 Demonstrate an understanding of critical points and absolute extreme values of a function
B16 Find the intervals on which a function is increasing or decreasing
C5 Apply the First and Second Derivative Tests to determine the local extreme values of a function
C6 Determine the concavity of a function and locate the points of inflection by analyzing the second derivative
B17 Solve application problems involving maximum or minimum values of a function
B15 Demonstrate an understanding of critical points and absolute extreme values of a function
B16 Find the intervals on which a function is increasing or decreasing
C5 Apply the First and Second Derivative Tests to determine the local extreme values of a function
C6 Determine the concavity of a function and locate the points of inflection by analyzing the second derivative
B17 Solve application problems involving maximum or minimum values of a function
activities
- Functions and Their Derivatives Activity from Desmos - In this activity, students will practice matching a function to its first and second derivatives. Then they'll create their own function and after successfully matching it to its derivatives, submit it into the gallery as a challenge for their classmates to solve. Inspired by Sandi Yoder.
- Concavity and Points of Inflection (video) from Brightstorm - A very well produced video from Brightstorm.
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- Curve Sketching with Derivatives (video) from Brightstorm - Another great video from Brightstorm.
- Functions on the Floor from Liana Dawson - An activity for small groups of students to understand first and second derivatives. Create an x and y axis on the floor with painters tape. Provide students with a collection of conditions on derivatives and second derivatives. Give students a piece of rope (or perhaps a jump rope) to create a graph with the given conditions.You could make this a series of stations around the room to work through.
- Curve Relationships Project from Jonathon Clayton - Jonathan describes a project where students create a 5th or 6th degree polynomial to be the derivative of a function. Then students analyse this function to determine the original function.
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- Jumping Rope to Understand Rolle's Theorem and Mean Value Theorem from Jeannette Cleveland - An activity that gets students skipping!