How can I use calculus to graph f(x)= 10(ln(ln(x))/ln(x))?

[NonTradHaruka]

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.

 

[Mark44]

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?

 

[NonTradHaruka]

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.