Tuesday, December 13, 2016

Tangent Line Approximation Discovery

You guys, what is it with me and blogging this year? What are your best tips when you feel like you just can't get into a groove with your blog?! I miss it! 

We just wrapped up our applications of derivatives unit in AP Calc and I wrote this little activity to introduce local linearization and tangent line approximations. It's one of the simplest but most important ideas in all of AP Calc- that if we look close enough, a tangent line at a particular point will be almost the same as the function since functions are locally linear

I knew my kids were more than capable of discovering this phenomenon and explaining it to each other without much help from me, so I wrote up this very simple activity for them:

We wrapped up with a discussion about what students had discovered, focusing heavily on part (f). I love seeing kids have these "duhhhh" moments- when something seems so simple that it's barely worth mentioning. It reminds me of those moments in college when a professor calls something trivial that was anything but trivial to you. When my students can start to view concepts in Calculus as so obvious they barely deserve explanation, I'm a happy teacher. 

Here's a link to the document! 


  1. Thank you! this is perfect. You nailed it, a beautifully simple concept but also a source of anxiety in my calc classes year after year

  2. Cany you tell me the answer to this?