Recitation 6

Recitation 6 (The Derivative Function)

Objectives:

• Students should be able to interpret and estimate instantaneous rate of change as the tangent line using a graph.
• Students will be able to use the limit definition of a derivative.

Important Notes:

• (5 minutes) Welcome the class to recitation. Ask students if they have filled in the notes section of the packet. Tell students that they should be filling in the notes section before coming to recitation.

• (10 minutes) Have students do Problem 1. You may need to do one or two points on a document camera to help the students get started.

• (10 minutes) Have students do Problem 2 and 3. Don't get caught up in differentiability at this point. The idea is to focus on what the derivative function looks like where it is defined. Particularly on problem 3 we expect students to finish with a piecewise function.

• (10 minutes) Have students do problem 4. Make sure they do all the calculations including expanding the cubic. These problems should help them realize the utility of the rules they are learning and prepare them to solve a problem just like this on the exam. In fact, you can tell the students that nearly every exam for the past several years has had a problem just like this on it.

• (15 minutes) Have students do Problem 5 and then present their methods for solving problem 5.

• (10 minutes) Have students do problem 6. Make sure they simplify before taking their derivatives. Nobody should be using the product or quotient rule at this point.

• (10 minutes) Have students do problem 7 and 8.

• (10 minutes) Have students do problem 9 and 10.

Notes:

• If this is being paired with the derivative graph matching activity then skipping problems 3 and 9 saved some time and didn't seem to skip any important concepts.
• Students were very confused on Problem 6. If you work that problem then expect to work it together or at least discuss with the groups.