MA 121 Sec. 005
R. Watson. 11 February, 2009
U.S. Unemployment Rate Example of Second Derivative Test.
US Unemployment Rate in Months Since January, 2007, To January, 2009.
Source: http://www.economagic.com/em-cgi/data.exe/feddal/ru
The list below consists of the unemployment rates for each month:
In[1]:=
The following command generates a best fit quadratic function and calls it f(x).
For more on best fit curves, see section R.6 in the text (p. 74).
In[25]:=
This is the function:
In[26]:=
Out[26]=
Unemployment for the 25 months from Jan 2007 to Jan 2009.
In[27]:=
Out[27]=
The Derivative of f(x):
In[28]:=
Out[28]=
Find the relative extrema. This command will solve for x in the equation f '(x) = 0, and assign the solution to the name "soln".
In[31]:=
Out[31]=
Is it a relative min or max? Plug "soln" into the second derivative and check the sign.
In[32]:=
Out[32]=
f''(x) > 0 for this particular x, so by the second derivative test, this is a minimum.
This means there is no relative max.
Hence, this model suggests no maximum unemployment rate!
(But we know there has to be a max, since the rate can't exceed 100%).
This model needs improvement.
