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Homework Help: Critical Points of Log Function

  1. Dec 19, 2011 #1


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    1. The problem statement, all variables and given/known data

    http://i.minus.com/jCH20SF290QIb.png [Broken]

    2. Relevant equations

    Critical point: when the derivative = 0 or the derivative fails to exist.

    3. The attempt at a solution

    I got x = 0 and x = e as critical points.

    When x = e, the function becomes 0 / e, which = 0. Therefore, e is a critical point of f.

    When x = 0, the function becomes 1/0, which = ∞. The derivative of ∞ does not exist, so wouldn't x = 0 be a critical point?

    The answer key disagrees; the only critical point the key provides is x = e.
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Dec 19, 2011 #2
    the key to this problem is in the first line: "for all x > 0". Log(x) is not defined for any x ≤ 0
  4. Dec 19, 2011 #3


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    Actually, it's the fact that f is defined only for x>0 that matters. If the problem said f(x) = (ln x)/x for all x>10, f would have no critical points.
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