Derivatives in the news
The Obama administration has been touting this graph:
So what does this graph show? The graph shows the job losses per month (non-farm jobs, adjusted for seasonal effects) with the upward bars representing job gains; one can clearly see that the economy is losing fewer jobs per month now than it was prior to the stimulus bill being signed. In short, this is the graph of the rate of change of the number of jobs per month; in short, this is a calculus derivative.
In “line” format the above graph corresponds to this one:
So, what does the actual jobs graph look like? Here it is (graphed in a “smoothed out” form):
Note: the vertical line signifies when the stimulus bill was signed into law (February 17, 2010). The units are in thousands.
Of mathematical note is the “negative peak” of the jobs loss graph: it corresponds with the change in the concavity of the jobs graph; the graph goes from being “concave down” to being “concave up”. Of course, the hope is that the jobs graph will eventually go up and not merely level off.
Of course, it is possible for jobs to go up and unemployment to go up at the same time, say, if jobs are being created more slowly than the workforce is expanding.