Nope, it states that the ratio for the line describing Laptop 65 can be found to be of the general type f(x) = sqrt(x) with the red dot located at the time of his demotion. The function isn't derivable at the red point but that isn't the point.
so you're saying that over time (barring deleted posts) his awesomeness was constantly rising, approaching infinity (albeit in a slowing manner) until he was demoted, at which point the function changed into something like g(x) = -0.1x.
using this information, we can calculate the peak of his awesomeness, his current awesomeness, and the average.
first, what we know:
laptop was demoted 6 months ago, assuming his posts per day was about the same as now, he had
posts = ppd * time = 7.5 posts/day * 684-182.5 days = 3761 posts
therefore, the maximum value of his awesomeness was, just before his demotion, f(3761) = sqrt(3761)
=~61.3.
immediately after demotion, his awesomeness PLUMMETED to g(3761) = -0.1*3761 = -376.1.
at the time of this post he is at g(5229) = -0.1*5229 =
-523.
that's a *awesomeness of nearly 600 in a relatively short period of time. not good, man.
his average awesomeness is (excuse the shitty formatting of definite integral limits)
(integral of f(x) + integral of g(x)) / posts
(0∫3761 f(x) dx + 3761∫5229 g(x) dx) / 5229 =
(0
/3761 (2/3)*x^(3/2) + 3761
/5229 (-0.1/2)x^2) / 5229 =
((2/3)*3761^(3/2) - 2/3*0(^3/2) + (-0.1/2)*5229^2 - (-0.1/2)*3761^2) / 5229 =
~
-96.8
q.e.d laptop's a fag