Derivative in interesting way I am supposed to give a 15-20 minutes math lecture, where I am expecting around 20-30 people. The lecture is about derivative. Since this would be my first "class", I would appreciate any suggestions to how to make it interesting. Students could be bored with definitions, theorems, mathematical concepts that are told in abstract way, therefore my question is: How to tell a story about derivative in simple, interesting but also, mathematically based way? :) Any suggestions about mathematical questions, examples, fun problems related to this topic (which should grab their attention) are also welcome.

Like the good Monsieur Jourdain who didn't know that he spoke prose all his life, you could point out that many in the audience have already seen the derivative many times daily, particularly if they are from well-to-do homes: namely, the speedometer of the family car.