Working through a differential equation problem from the 2015 BC calculus exam

I’m using old problems from the BC Calculus exams to make sure I’m pitching the course at the right level. A few of the old questions have surprised me, but many are really nice problems.

This differential equation problem from the 2015 exam was a nice way to explore some basic ideas about derivatives with my son:

We started by reading the question and then drawing in the slope fields:

The next question asked you to find the 2nd derivative in terms of x and y only, and then asked you to talk about the concavity of solutions to this differential equation in the 2nd quadrant:

The third part of the question asked about a solution to the differential equation at a specific point – in particular if that specific point was a maximum or minimum:

Finally, a pretty neat question about a linear solution to the differential equation. Unfortunately I forgot to zoom out after reading the question – hopefully my son’s words explain what he’s doing:

I thought this was a really nice introductory differential equation problem – it was nice to see that we could talk through it even though we haven’t really talked about differential equations formally, yet.