U1S1V12 Zero derivative.txt

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We've calculated f prime of 2 to be 0 meters per second.
But what does that mean?
Should we interpret it as saying that the pumpkin froze
in midair?
Well, no.
We know that pumpkins don't behave like that.
Freezing in midair would require the velocity of the pumpkin
to be 0 over a period of time.
But what we have is a derivative.
That's an instantaneous velocity.
So it's a velocity only at the instant t equals 2 seconds.
To think about it a different way,
we know that a positive derivative
means that f is increasing.
So the velocity would be upward.
A negative derivative means that the velocity would be downward.
There's an instant, however, in between.
Right at the time the pumpkin reaches
the top of its trajectory.
The pumpkin has stopped going up.
But it hasn't quite started to go down.
And it's right at that moment that we
say that the instantaneous velocity is 0.