Recitation 14

Recitation 14 (Linear Approximation)

Objectives:

• Students will be able to write a linear approximation to a function as a tangent line.
• Introduce logarithmic differentiation.
• Reintroduce hyperbolic trigonometry.

Important Notes:

• This is a long lesson and you will probably not make it through the entire packet in this class.

• [ (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.

• [ (5 minutes)] Have students work together on problem 2. Students should have seen very similar problems in lecture and should be able to do the problem without a lot of struggle.

• [ (5 minutes)] Have students work together on problems 3 and 4. These problems are basically asking for exactly the same information. We want students to recognize either way of asking this question.

• [ (10 minutes)] Have students work together on problems 5 and 6. You will almost certainly need to refer students to their notes on the MVT and point out what the hypothesis and conclusions are.

• [ (10 minutes)] Have students work together on problem 7. Students usually struggle to see exactly how to apply the MVT, you should expect to have to ask them leading questions.

• [ (10 minutes)] Have students work together on problem 8. Make sure that students test all aspects of the racetrack principle to solve this problem.

• [ (15 minutes)] Depending on how things go you might need to prepare a couple of examples to do at the end of class to wrap things up and tie it all together. Prepare examples about linear approximation instead of the theorems as the theorems are something they need to practice with on their own.