Do we include asymptotes as critical points?

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Discussion Overview

The discussion revolves around whether asymptotes should be considered critical points in the context of the function y = x sqrt(4-x^2). Participants explore the implications of including asymptotes in the analysis of critical points, particularly in relation to graphing the function.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions if asymptotes should be included as critical points, citing the function y = x sqrt(4-x^2
  • Another participant suggests that points where the function is not differentiable, such as asymptotes, should be considered critical values, while also noting the domain restriction of the function.
  • A later reply reiterates the initial question about the necessity of including asymptotes for graphing the function, emphasizing their role in defining the graph.

Areas of Agreement / Disagreement

Participants express differing views on whether asymptotes should be classified as critical points, indicating that the discussion remains unresolved.

Contextual Notes

There are limitations regarding the definitions of critical points and the treatment of asymptotes, as well as the implications of differentiability in this context.

LadiesMan
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I was wondering if we include asymptotes as criticals:

For example in y = x sqrt(4-x^2)

when u find the critical points it gives u root 2 and negative root 2

But when I draw the graph I am missing the 2 and -2 which were the asymptotes which help define the graph?

So are they needed?

Thanks
 
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In general, a point that is not differentiable should be considered a critical value. However, the domain should be { x,-2 \leq x \leq 2 }. In other words, \sqrt{0} is defined.
 
LadiesMan said:
I was wondering if we include asymptotes as criticals:

For example in y = x sqrt(4-x^2)

when u find the critical points it gives u root 2 and negative root 2

But when I draw the graph I am missing the 2 and -2 which were the asymptotes which help define the graph?

So are they needed?

Thanks

You may use the vertical lines x=2 and x=-2 to help you draw the curve in that the graph of this function becomes vertical at those points.
 
yay thank you!
 

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