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Math Help - Critical Points

  1. #1
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    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
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  2. #2
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    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?
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  3. #3
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    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
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  4. #4
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    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.
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