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Critical numbers of this derivative

  1. Nov 24, 2005 #1
    I have the function [tex] \[y = \sqrt x - 4\ln (x)\][/tex]

    I find the derivative to be [tex] \[y' = \frac{{\sqrt x - 8}}{{2x}}\] [/tex]

    When finding the critical numbers of y' I look for where the derivative
    is equal to zero or where the derivative is undefined. So where y' is
    equal to zero is when x=64. y' is undefined when x=0, but when x=0
    the original function is also undefined. Since x=0 makes the original
    function undefined can I exclude it from my critical points? I am thinking
    I am able to since x=0 isn't even in the domain of y.

  2. jcsd
  3. Nov 24, 2005 #2


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    Yes, that is correct. By the way, the phrase "critical numbers of y' " is not correct. What you have found are the critical numbers of y itself, not its derivative.
  4. Nov 24, 2005 #3
    Thanks HallsofIvy :smile:
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