Mean Value Theorem Free Response Critique

Every year the justification of Mean Value Theorem is something we spend a lot of time finessing (a new favorite word of the senior class here...any other schools seeing this?) over the course of a year in AP Calculus. The students understand the concept, but struggle with accurately justifying the situation. We started MVT last class and as a warm up today I did this activity with them. 

I gave each set of partners about 5 minutes to complete the front page and then we discussed- what are the "giveaways" that you should be thinking about MVT? What are the conditions that need to apply? How would YOU answer this? 

Then, I had them flip over to the back and do a critique of 3 arguments with their partner. Each one could some tweaking, although one did receive full credit on the AP Exam. 

The third section I left blank intentionally, so I could move around the room and see what students were putting on the front side of the page. This way they could critique their own answers in light of the responses they saw. Here's what I had them write in based on what they were writing with their partners:

We got to discuss the importance of using the same notation for the function in the problem (using g, not f) and the importance of the justification part. 

Here's the activity! 

MVT Partner Critique

We will be building on this next class as we spend an entire day trying to differentiate between when to use which existence theorem and looking at some more interesting AP style questions. Feel free to send any suggestions or other favorite MVT activities my way!