I started making a sketch to look at local linearity, and I found that Sketchpad does not make it easy to zoom in on points besides the origin. I tried the "dilation arrow" technique, but that doesn't seem to work for functions. Under certain conditions I could get the function to zoom in and out, but the tangent line seemed to jump around quite a bit. Maybe I'm missing something. In the end, I made a series of buttons that moved the axes and hides one curve and shows another, it's a bit complicated.