>>13725385Let f(x) be a real function, f'(x) it's derivative, defined on [a, b], with f(a) = f(b).
note that: integral from a to b of f(x)f(x)'dx = 1/2 [ f^2(b) - f^2(a) ].
Note that the average value of f' on [a, b] is: 1/(b-a) integral from a to b f'(x)dx = (f(b) - f(a))/(b-a) = 0.
The correlation between f(x) and f'(x) over [a, b] is :
1 / ( b-a) integral from a to b of f(x)f(x)'dx / Sqrt(1 / ( b-a) integral from a to b of f(x)'^2dx * 1 / ( b-a) integral from a to b of f(x)^2dx ) = 0.
You cant even find the correlation between a function and it's derivative over and interval if the average value of derivative over that interval is 0. This is pathetic. Why would defend this crap and the broken tools they use?
