Discussion Overview
The discussion centers around the existence of a derivative at vertical asymptotes, specifically examining the function 1/(x^2) at x=0. Participants explore the implications of a function being undefined at certain points and how that affects derivative existence.
Discussion Character
- Conceptual clarification, Technical explanation
Main Points Raised
- One participant questions whether the derivative at a vertical asymptote can be infinite or simply non-existent.
- Another participant asserts that for a function to have a derivative at a point, it must be defined at that point, indicating that since 1/(x^2) is not defined at x=0, the derivative does not exist.
- A later reply reinforces the idea that if the function is not defined at a point, then the derivative cannot exist there.
Areas of Agreement / Disagreement
Participants generally agree that if a function is not defined at a point, then the derivative does not exist at that point. However, there is some uncertainty regarding the nature of the derivative at vertical asymptotes.
Contextual Notes
The discussion does not address the broader implications of derivatives at vertical asymptotes or any potential exceptions, focusing solely on the specific case of the function 1/(x^2).
