Detect a single inflection point of the given.

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Hi everyone, I was wondering if someone could help me a little to find the tipping point of that data series automatically, as data can change.
x = [15 14 13 12 11 10 9 8 7 6 5 4 3 2 1];
y = [0 1 0 1 0 0 22 49 201 255 255 255 255 255 255];
The data represented are those shown below
df1 = gradient(y,x)
df2 = gradient(df1,x)
figure
plot(x,df2,'-o','LineWidth',2)
hold on
yline(0);
But now i don't know how to decide which is de correct inflex point of these data.
  • It must be just 1
  • It must be on the given points
  • In this case it has to be or the point (7,201) or (8,49)
I have looked in [1], [2], [3], [4], but i couldn't solve my problem.
Thank you for all.

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