Finding the inflection point in pandas DataFrame

Question

I have a two column DataFrame with just a list of numbers in x and then a monotonically decreasing -but not constant- set of numbers in column y

data

    x        y
0   1   600.000000
1   2   222.361705
2   3   139.820496
3   4   114.353763
4   5   90.807283
5   6   80.022188
6   7   72.193116
7   8   62.309712
8   9   55.362476
9   10  47.335051
10  11  42.821741
11  12  40.540734
12  13  37.758571

What I'd like to try is find for what x value is the inflection point in y. I've tried a few different methods of people asking similar but not quite the same question, but they're not quite working.

dy = np.diff(data.y) 
idx_max_dy = np.argmax(dy)

But I know that's not right, and I'm running into dimensionallity problems. Any suggestions would be appreciated.