Calculus: Getting It Straight – Differentiability as Local Linearity

The study of average rates of change and slopes of lines begins early in a student’s math trajectory.

Calculus begins the study of instantaneous rates of change, and zooming in on the graph of a differentiable function is an intuitive way to get at the corresponding idea of local slopes. The idea that a differentiable function behaves locally like a linear function is profound and important.

In this webinar, the leaders will:

• Highlight the importance of differentiability as local linearity and zooming as a means of exploring the derivative at a point
• Tie the application of local linearity to L’Hopital’s rule (new addition to the AB calculus course description)
• Connect the local linearity idea to linear approximations, to slope fields and to Euler’s method