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.