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Best technique for determination of the bend in a curve

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Dear Collaboratory,

I have a problem that I cannot resolve. I would like to determine the bend point in a curve. Strange enough my approach seems to work quite well for some curves but fails completely for others. I have to questions: (1) is there a better method to define the bend point? and (2) what is the cause that it sometimes works fine and fails another time (although the curves do not differ too much)

Thank for your help and input with this problem.


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