1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Critical Points of Log Function

  1. Dec 19, 2011 #1

    Qube

    User Avatar
    Gold Member

    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

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Critical Points of Log Function
Loading...