Calculus: Getting It Straight – Differentiability as Local Linearity
Technology: TI-84 Plus family, TI-Nspire™ Technology
Topic: Teaching Resources
Speakers: Tom Dick, Dan Kennedy
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
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