How to recognize discontinuity of slope in numerical data

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I am dealing with a set of data that, when plotted, shows a breaking point as shown in circles. How can I identify these points in the data without needing to plot them every time? I tried looking for discontinuity in the sllope, but that did not help.

Accepted Answer

Walter Roberson
Walter Roberson on 11 Sep 2021
Take the second derivative --
d2y = gradient(x,gradient(x,y))
Look for the spot where the second derivative changes from negative to positive.
  1 Comment
Saeid on 11 Sep 2021
Thanks Walter. I guess that will help, but I guess it is gradient(gradient(y,x),x)

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