What a kid learning calculus can look like

My older son is working through Stewart’s Calculus book this year (edition 3). Right now he is working on one of the introductory derivative sections. Today I picked to problems from that section and asked him to work through them live.

Here’s the first problem -> a problem about finding a line perpendicular to a parabola:

Here’s the second problem -> a problem about a piecewise defined function. I was using this problem to introduce the concept of “differentiable”. Although we had not discussed that definition ahead of this problem, he was able to reason through what it meant.

I think this is a really nice example of a kid working through a challenging problem.