- Pick a point on e^x and draw a tangent line.
- Estimate the slope of that tangent line by counting boxes.
- Plot that slope on the blank axes below.
- Keep doing this until you have a picture of the derivative.
This is one of the most frustrating activities that I do in my Calculus class, because I get so frustrated trying to explain what I should be a fairly easy idea if you have been differentiating for 5 months, but I keep doing it anyway. I guess I just think it's so important in the conceptual understanding of the derivative, and it makes me realize that I need to keep hammering home the big idea of a derivative. I know a GeoGebra derivative tracer could do this in half of a second, but part of getting them to do this is that the picture comes out really slowly so that they have time to think about this mystery of a function having its own derivative, and is a really easy way to then start talking about how at every point of the graph of e^x the y value and the slope are equal to each other.