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.

 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.

 Jumping Rope to Understand Rolle's Theorem and Mean Value Theorem from Jeannette Cleveland  An activity that gets students skipping!