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Homework Help: Simple Natural log graph?

  1. Nov 6, 2009 #1
    1. Graphing Carefully: Sketch f(x)= 10(ln(ln(x))/ln(x) accurately using calculus, your calculator, or both to aid you. Make sure to include all vertical asymptotes, as well as local extrema

    2. f(x)= 10(ln(ln(x))/ln(x)

    3. OK. I might come across as stupid but here goes... I don't know what to do. I looked at the graph and figured 'what is there to show?' besides a VA. So I came up with VA=1, x-intercept=2.71828, and the local max is (15.1543, 3.67879. But how do I get this with calculus? I solved for f'(x) but I do not know how to work this stuff to find/prove the max and increasing/decreasing, concavity,etc. HELP, please. Thank you.
  2. jcsd
  3. Nov 6, 2009 #2


    Staff: Mentor

    You can do all of this without a graphing calculator. For the vertical asymptote, where is the denominator zero? For x-intercepts, where is the numerator zero? For max value/min value, where is the derivative of the function zero? For where the function is increasing/decreasing, where is the derivative positive/negative? For where the function is concave up/concave down, where is the 2nd derivative positive/negative?
  4. Nov 6, 2009 #3
    Thanks for the reply Mark44.

    I worked it out! I think I made it harder that it was... a lot harder than it was.

    Thanks for your help.
    Last edited: Nov 6, 2009
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