Calculus students spent today manually finding the “slope function” for a third function. On really large poster paper, they worked in groups to find the derivative of f(x)=1/3*x^3 by drawing tangent lines, estimating the slope and then plotting the result. Most groups ended up plotting a parabola after 15 minutes or so, so they guessed that the derivative of 1/3*x^3 is x^2. Great!
And then a couple students asked the question, as if on cue, “Isn’t there an easier way to do this?” Another student was adament that he had a rule that worked, but it only seemed to work in a few cases. So then we embarked on the quest to find rules for derivatives. To accomplish this, we used a derivative tracer on GeoGebra to trace out the derivatives of a bunch of functions. Students got started with this today, and will probably use most of class tomorrow too to start looking for patterns. Goal by the end of class tomorrow: the power rule!
In AP, we explored local linearity, and motivated the need to look at functions on a micro scale, which is why tomorrow we will start exploring limits.