00:01
The question gives us a table of us unemployment rate u of t from 2003 to 2012.
00:06
It asks us to interpret what uprime of t means and also to estimate its values at each year.
00:13
For part a, uprime of t is the derivative of u of t, and if u of t means the rate of unemployment in the u .s., its derivative is the rate of change of unemployment in the u .s.
00:38
And now for part b, i've already gone ahead and put the values in the table in a graph, so now all we have to do to find the derivative at each point is find the slope of the tangent line at each point.
00:49
My drawing isn't perfect, so my tangent lines won't be exact, but i will give the correct value for each slope.
00:57
So to start, we can go to 2003 and then draw the tangent line at that point, which looks something like this.
01:09
You can make that more accurate.
01:13
And so the value of u prime of t at 2003 comes out to be nymph.
01:19
Negative 0 .5.
01:22
And again, the way that you'll find that is by taking the rise over run of the tangent line that you draw, and the slope will be your answer.
01:33
So next for 2004, the tangent line looks something like this...