The Derivative Function (Lesson 9.3 Day 2)
Unit 9 - Day 6
Define a derivative as the slopes graph of an original function
Understand that the derivative is itself a function that outputs the slope of the curve at any x-value
Find an equation for the derivative function using the limit definition of the derivative
Use derivative notation to refer to derivative functions and derivatives evaluated at a point
Quick Lesson Plan
In today’s Round Table activity, students should be in groups of four. Each group member gets a different question and has to solve part a (evaluate function). After an allotted time (2-3 minutes), they must rotate papers so they are working on a new problem. After checking the work of their peer in part a, the student completes part b. Students should not move on even if they are done before the given time (we suggest 3-4 minutes). This continues until parts a-d are done. Allow for slightly more time on each part since students must check the work of everyone before them. Part c will take the longest, so plan on giving 8-10 minutes for students to simplify the difference quotient and take the limit. Have students affirm or high-five each other as they pass papers to build class community. At the end, have students look at their original paper to review the solution. Give students 3-5 minutes to ask each other any questions they had while solving.
The idea of a derivative equation is still fairly new to students and it takes time to solidify this understanding! Mastering the mechanics of evaluating the limit of the difference quotient is important, but even more emphasis should be placed on interpreting the meaning of this new function. Subsequent lessons rely on students having a firm grasp of what a derivative function is and does. Continue to ask students to interpret values on a derivative graph.