Do we include asymptotes as critical points?

[LadiesMan]

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

 

[amolv06]

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.

 

[arildno]

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.

 

[LadiesMan]

yay thank you!