U1S1V11 Negative derivative.txt

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In our last video, we threw a pumpkin off a building.
And its height was given by this function of time.
We calculated these derivatives, f prime of 1
was 10 meters per second and f prime of 3
was minus 10 meters per second.
So what does that mean?
Let's think about where this pumpkin has been,
where its position has been.
So at time t equals 0, we have that f of 0 is 100 meters.
So that's the height of the building.
That's where the pumpkin starts.
And we also calculated in the last video that f of 1
was 115 meters and f of 3 was also equal to 115 meters.
So if we think about it, we can figure out what's going on.
If 115 meters is here, then at t equals 1 second,
the pumpkin is at that height on its way up.
And at t equals 3 seconds, the pumpkin
is, again, at that height, but this time it's on the way down.
And eventually it goes splat.
So f prime of 1 is positive because it's
measuring the instantaneous velocity when
the pumpkin is moving upwards.
Or other words, the height f is increasing.
Whereas f prime of 3 is negative because it's
measuring an instantaneous velocity
at a time when f is decreasing, the height is going down.
So the sign of a derivative tells us
the direction in which the function is changing.
If f prime of a is positive, then f
is increasing at that point.
And if f prime of a is negative, then f
is decreasing at that point.

We have one other thing to talk about.
But first, we want you to get some practice calculating
derivatives.
So why don't you calculate f prime of 2?
And then we'll come back and discuss.