1. ## Critical Points

Determine the critical points for this function: x/x^2-1.

The answer is that there are no critical points, but i dont see how that is possible

2. ## Re: Critical Points

Well, I guess the first question is, "what do you think a 'critical point' is?" What definition are you using? What points do you think would be critical points?

3. ## Re: Critical Points

i thought any number where f '(x) is 0 or does not exist created a critical point. Assuming that I did the first derivative correctly the denomenator would be (x^2-1)^2 causing both -1 and 1 to not exist

4. ## Re: Critical Points

I suspected that. First, a value of x is NOT a critical point. A critical point is a point, (x,y), on the graph of the function, such that the derivative is 0 or does not exist. Here, x= 1 or x= -1 does not give a critical point because there is no point on the graph of y= f(x) which x= 1 or x= -1.