That this month's rate is smaller than expected is a completely different thing to it being smaller than last month's rate.

Second derivative I think. Inflation is change in prices. Change in inflation is a second order derivative? I wish more Americans knew at least a little conceptually about derivatives. Personally, I need to review them. Anecdotally, the number of accountants that I've met that haven't progressed beyond middle school level math is depressing as well.

I think it's second derivative.

3rd derivative would be Nixon's:

>When campaigning for a second term in office, U.S. President Richard Nixon announced that the rate of increase of inflation was decreasing, which has been noted as "the first time a sitting president used the third derivative to advance his case for reelection."[2] Since inflation is itself a derivative—the rate at which the purchasing power of money decreases—then the rate of increase of inflation is the derivative of inflation, opposite in sign to the second time derivative of the purchasing power of money. Stating that a function is decreasing is equivalent to stating that its derivative is negative, so Nixon's statement is that the second derivative of inflation is negative, and so the third derivative of purchasing power is positive.

https://en.wikipedia.org/wiki/Third_derivative#Economic_exam...

Second derivative:

  p = price
  t = time
  dp = change in price
  dp/dt = change in price over time = inflation
  d^2p/dt^2 = change in change in price over time over time = change in inflation over time = what we are talking about

What would the fourth derivative of inflation be? I can’t get my brain to work for that.

No, acceleration is going down. Not a lower rate of acceleration. The second implies acceleration is still increasing, but at a slower rate. What is actually happening is we're decelerating (so we're still going fast, meaning inflation is high, but inflation is going down...)

Without trying to be mean, I would also argue your framing is also poor as some inflation is not bad.

To put it in context, if current trends hold we'll expect 3-5% inflation yoy. That is not awful. Higher than last decade or so but we have had super low inflation for a long time. Averaging out, inflation over the last decades, even including the recent high inflation, will still be pretty low, around 3%.

The velocity has slowed.

Also there isn't a cliff, there's only speed bumps for going too fast. At least if movement=inflation.

On the other hand if the "cliff" is supposed to be a specific level of inflation, then we didn't just slow down, we're walking away from it.

There's no cliff (at least for this to be the third, or even second, derivative with regard to.) Its not like there is a magic bad nominal price level.