Graph oddity

03022016, 06:59 PM
Post: #1




Graph oddity
When plotting 1/sqrt(9*x^2 + 4), Prime will not find extremum of (0,.5) unless x<~.47
Further from X=0, Prime comes up with NaN. 

03022016, 07:16 PM
Post: #2




RE: Graph oddity
I suspect that's because the algorithm for finding the extremum uses the 2nd derivative of the function to select intervals for search.
Using the Prime, I found the 2nd derivative of the function you mentioned, and found it's roots at sqrt(2)/3 and sqrt(2)/3, which are roughly equal to 0.47 and 0.47. These are the places where the function's curvature goes from positive to negative (inflection points). The extremum function probably searches the intervals (inf, 0.47), (0.47, 0.47) and (0.47, +inf) for places where the first derivative is equal to 0. Since the first and last intervals listed never reach a place where their slope is zero, the extremum function's search fails if you start in those intervals. Starting somewhere between 0.47 and 0.47 allows the function to search that interval, where it does find a solution. Truthfully I have no clue how the extremum function works, but that's how I'd program it if given the task. 

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