U1S6V13 Headline news.txt

#
# File:   content-mit-18-01-1x-captions/U1S6V13 Headline news.txt
#
# Captions for MITx 18.01.1x module [GqMvzs22ZUo]
#
# This file has 49 caption lines.
#
# Do not add or delete any lines.  If there is text missing at the end, please add it to the last line.
#
#----------------------------------------

Let's take a really close look at this headline--
"Rate of Job Growth Slows."
We'll start with the word slows.
You hear that and you think, this
isn't so good for the economy.
So something has gone down.
But what exactly?

This is where we need to be very precise with our language.
So let me introduce a function f.
And that's going to give us the number
of jobs as a function of time.
But it's not f that's gone down.
The headline says that the rate of job growth
is the thing that's slowed.
f is the number of jobs, it's not a rate.
So instead, the headline is referring to f prime.
f prime is the rate of change of the number of jobs.
And it's that rate which has gone down.

How exactly has it gone down?
Well, the key is this word growth.
That implies that the number of jobs has been growing.
So the rate of change in the number of jobs, f prime,
has been positive.
It may have been something like plus 200,000 jobs per month
in the first quarter.
And then in quarter two, the headline
is saying that there's still job growth.
f prime is still positive.
It's just slower than the previous rate of job growth.
So it might be something like plus 100,000 jobs per month.
If we graph f, then over the course of the first quarter,
we know that it increased at a certain rate.
And then over the second quarter,
it again grew, but at a slower rate.
So if we draw just a curve connecting these three points,
then we see that the graph of f is concave down.
And this should make some sense, because f
prime is the thing that's decreased.
And if f prime has decreased, then f prime's
derivative, f double prime, should be negative.
So f is concave down.
So that's a little lesson in why we
need to be careful with our language
when we're describing rates and derivatives in the real world.
We've got some other questions to help you practice that.