Strawman?

Hardly.

• You said 2nd derivative was no good and that 1st derivative was the way to go.
• I demonstrated that neither is a good mechanism for the data in question.
• You countered: "your graph is upside down" -- a strawman if ever.
• I demonstrated that of the 7 inversion points in the data; first derivative only sees 5 of them. And of those 5; three are substantially inaccurate.

  Indeed, if you draw a few vertical lines on your own linked graph -- which is now at least accessible -- you can see both problems: missed turning points and inaccurately discovered ones.

The age old problem with first (and second) deritives -- along with many other numerical methods -- is that they have a tendency to discover values that don't exist in the dataset. Ie. calculated values that fall between the discrete values that are actually in the dataset.

Whilst this is fine for theoretical discussion -- rounded to some number of sig.fig. -- it leaves real-world applications with the need to fall back upon heuristics -- ie. guesses -- in order to "correct" calculated values and align them with the actual data.

Imagine the dataset represents clock-speed (or power drain) from a deep-bin sort of newly minted cpus. -- ie. when cpus are manufactured, there is some considerable variability in their electrical performance; and manufacturers can sort the parts by their actual performance, and charge premium prices for the better ones.

In the many all-too-real scenarios like this that crop up in manufacturing every day, having calculated maxima and minima that fall at theoretical points on the curve; between the actual values that are there, isn't very useful for the selection processes that are the reason for performing the calculation in the first place.

So no, not a strawman. A legitimate and relevant discussion in context.

I accept that my original graph was, as presented, difficult to interpret. But I anticipated that anyone interested would

1. produce their own graph to verify the accuracy of my quick plots and conclusions.

   Which you did.

2. Inspect their own plots carefully and notice the obvious discrepancies that I noticed in mine.

   Which you did not.

That's the trouble with "pretty graphs". People get so impressed by the pictures, they forget to inspect them closely and take note of why they produced them in the first place.