## 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!

#### 2 comments:

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?