If the curve of f'(2) aproaches negative infinity, ie vertical asymptote. Can we consider x= 2 to be a Critical number?

Question

anonymous · Answer

I mean to ask if f'(x) at x=2 aproaches negative infinity (vertical  asymptote), can we consder x=2 to be a critical number of f(x)?

anonymous · Answer

@mathslover

vishweshshrimali5 · Answer

Yes you must take it to be a critical point.

anonymous · Answer

cool thanks so much, would it be fair to say that 2 would be a critical number but (2,-inf) would not be a critical point?

vishweshshrimali5 · Answer

Actually, you would consider x = 2 to be a critical point

vishweshshrimali5 · Answer

You can't say that (2,-inf) is a point as -inf is not a real number.

anonymous · Answer

so you see my confusion? But you can say x=2 is a critical number?

vishweshshrimali5 · Answer

Actually see, when you calculated f'(x), you started to find out the critical points right ?

anonymous · Answer

nope, i am just presented with a plot of f'(x)

vishweshshrimali5 · Answer

Okay so in that case, only say x = 2 is the value of x where f'(x) becomes underfined.

vishweshshrimali5 · Answer

*undefined

anonymous · Answer

and asked to mark down the values of x where the critical points of the original function are found

anonymous · Answer

hmm

vishweshshrimali5 · Answer

Well the critical points for f'(x) is x = 2.

But, for f(x), well that's a different case

anonymous · Answer

OK so I think this is only a  critical point if x=2 is part of the domain of f(x). But how do i know, if it is an asymptote at f'(2)?

vishweshshrimali5 · Answer

Well, sorry for I don't have much information about calculating asymptotes so I would just refer you to @ganeshie8 .

anonymous · Answer

ok thanks very much. Appreciate your help with my confusion.

vishweshshrimali5 · Answer

and may be @Kainui also. :)

vishweshshrimali5 · Answer

That was no problem at all. 

Good day :)

anonymous · Answer

good day to you too mate

anonymous · Answer

Still wondering if x=2 it is a critical number of f(x) , or if  (2,-inf) is a critical point of f(x), although my hunch is yes for the number but  no for the point. Since -inf can not really be considered to be the y-value of a point.

anonymous · Answer

Can someone please  confirm if my hunch is correct?

zepdrix · Answer

Yes you are correct.
We only use the x-coordinate to list our critical points.

If we want to further identify what type of critical point it is: maximum, minimum, or something else... then yes we might need to look at the coordinate pair.

But to say "critical point", yah x-coordinate is enough :)

anonymous · Answer

ok thanks a million!