Exploring Gradient Functions
What & why? A colleague was looking for ideas about introducing e. It can seem like it comes out of nowhere and the students struggle to relate it to what they already know. Maybe 15 years ago I was shown this activity using a package called Autograph. I don't know what happened to Autograph, but we have Geogebra now, so I've thrown together this slide to resurrect this activity, which is a little bit sticky has a little bit of aha. This slide is for introducing e^x and where e comes from and how it helps with differentiation. I would use it after teaching the chain rule and the product rule. Students will only have seen boring examples of these two rules involving polynomials so they won't really see the point in them yet. Link to GeoGebra Page 1) Plotting y=2^x and its gradient function Ask the students to plot the graph of y = 2^x on MWBs. ["Don't rub it off. Put your boards face up on the desks."] Teacher opens the Geogebra page. Make sure the graphs
