We began class with a selection from the reading entitled Why Do We Study Calculus? This led us to a brief discussion of the historical context for calculus and the derivative.
We defined the derivative as a rate of change. In particular, the derivative of a function at a point can be thought of as the slope of its tangent line at that point. Defining a tangent line was a little tricky, but we looked at one in Geogebra for the function
at the point (4, 3). We saw that as we zoomed in on the point (4, 3), we observed that the function was locally linear, and the tangent line and function were virtually indistinguishable. Thus, we defined a tangent line for a function to be the line that the function approaches as we zoom in closer and closer.
at the point (2, 5) using only our graphing calculators. While we found several lines that appeared to be tangent, the only line that was truly tangent was
We then stepped back and admired our work on the first day of calculus class: the derivative, tangent lines, local linearity. Impressive. For a different take on the tangent line, take a look at this website.
We talked a little about the structure of class. After each Red day class, the obligation is to attempt each problem in the assignment. The scribe will post the notes from class (scribe does not need to attempt each problem). At the start of the White day lab class, we will first revise the scribe's notes, and then we will go over the day's questions. Lab days will be the opportunity to finalize assignments which are submitted every two weeks.
