A true story
When I was in town the other day I accidentally found this graph in the gutter. It was very unhappy as it had forgotten who it was. The graph also told me it used to be most happy for a number between 2.5 and 3, but could not remember the exact number.
Can you bring identity and happiness to this graph? The phone lines are open and operators are standing by for your solution. Please call GRAPH-HELPLINE.
The photo of the graph was taken with the free software Maxima.
February 12th, 2010 at 1:38 am
Call the function f. I notice that f(x) appears to have its maximum at x ~~ e, and that f(2)~~f(4)~~sqrt(2). Trying to think of functions that have an extreme value at e, and corresponding values at 2 and 4, I remembered f(x)=x^(1/x). This appears to be it. 2^(1/2) = 4^(1/4) = sqrt(2). e^(1/e) ~~ 1.4446678610.