At school, if you do A-level maths, you will do calculus. One of the first things that you encounter are derivatives, which are the measure of the rate of change of some variable. Of course a derivative or rate of change may not be constant over time, so the second derivative will be used to show how the rate of change is changing over time.

With me so far? This may sound esoteric, but it turns out that second derivative headlines; such as changes in the rate of inflation (inflation is a first derivative, so changes in it are second derivative, are favorites for headline writers.

I decided to pick up ones that I spotted from the BBC web site, although special mention must go to

Hugo and I originally thought this was two second derivatives in one headline, but the first (unemployment rate slows) looks only to be a first derivative, because 'unemployment rate', is not a 'changing of one thing with respect to another' sort of rate, so not a first derivative.

24/2/09	East European worker influx slows	Influx us a first derivative, so if it changes, such as slows, its a second derivative
24/7/09	Pace of economic slide 'to ease' which was subsequently changed to UK economy continues to contract	Economic slide is a first derivative, so easing is a change in the slide over time: second derivative The new headline removes the second derivative component, and so removes some of the slighly more positive spin.
	Decline in UK car output slowing	Classic
28/7/09	First 2009 rise for house prices	A change in the rate of house price inflation is a second derivative
30/7/09	Swine flu incidence 'is slowing'	100,000 new cases last week, 110,000 new cases this week, so its still rising, buts apparently the amount that it is rising each week is going down. Second derivative. Indeed, when reported on radio 4, the newsreader said "The rate of increase is slowing down", which is as good a second derivative as you can get
10/8/09	Rate of job cutting 'is slowing'	OK if you interpret job cutting as the first derivative of the number of jobs.
13/8/09	England youth drop-out rate rises	A rate is almost by definition a first derivative, so if it rises, thats a second derivative
	Antarctic glacier 'thinning fast'	"One of the largest glaciers in Antarctica is thinning four times faster than it was 10 years ago." Thinning is a rate of change, so if it is faster now than 10 years ago thats a second derivative.
28/8/09	Decline in UK car output slowing	After a bit of a lull, a return to a classic first seen in July
14/10/09	Growth in UK unemployment slows	Couldn't be better
22/10/09	China economic growth accelerates	And another classic
9/11/09	Jobs market decline 'set to slow'	A good example of where you have to go to a second derivative in order to find a hint of good news in what is essentially still bad news. Don't be fooled... The jobs marker is still declining.
11/11/09	Rise in UK unemployment slowing	Much the same as the previous comment. In this case unemployment is still rising
12/11/09	Greenland ice loss 'accelerating'	Unlike the previous Eco-headline, the second derivative is clear in the headline
20/11/09	Decline in car output rate smallest this year	The headline on the front page was "Decline in car output slows". So in four months this is the third time we have had the headline, but still the car output slows..
16/12/09	UK jobless rise continues to slow	Again, using second derivatives to extract a crumb of comfort out of the worsening economic situation
23/3/10	UK inflation rate falls to 3% in February	Changes in inflation rate are always a good source of second derivatives