How to recognize discontinuity of slope in numerical data

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.

Answer 1

[Walter Roberson]

Take the second derivative --

d2y = gradient(x,gradient(x,y))

Look for the spot where the second derivative changes from negative to positive.

[Saeid]

Thanks Walter. I guess that will help, but I guess it is gradient(gradient(y,x),x)

Right?