Talking parabolas and calculus with my younger son

Because of a careless mistake I made last week asking my son to read a calculus-based section in the statistic book he’s studying, I’m doing a few light touch calculus projects with him. Today’s will likely be the most computationally heavy one as my main goal is simply to show him the ideas.

He mentioned to me yesterday that in his class at school they are studying graphing parabolas. I decided to use a quadratic for today’s calculus example. First I asked him to graph it. As the video shows, I probably should have asked him how they were approaching the problem in his class at school first!

Next we spent a few minutes finding the tangent line to our parabola at the point (0,3). Here we talk about what the tangent line is:

Here we finish the tangent line calculation:



Next we moved on to finding the area under the curve. We’d discussed a similar example earlier in the week, so I thought this part of the project would make for a nice review of that prior talk. We ended up diving a little deeper than I intended, but I still think it was a good discussion.

Here’s the introduction to the area problem:



And here’s the final calculation of the area: