Surprise! This is a hard topic for my students. I have adjusted some things and through various conversations I've had and pondering I've done, I came up with this activity that I tried today. This is after a couple of days of activity and discussions and problems related to:
If you see THIS on ____ graph, what does it mean about ______ function?
Here's what we did today for a while. I took it problem by problem and then we discussed it and for each problem I had them draw the "eggnog height vs time" graph after they had ruminated for a while. I also then introduced up and down arrows under the curve to represent "magnitude of rate of change".
In one class, we had a heated discussion about whether when you start or stop pouring, if it's an immediate leap to some rate of change or gradual.