00:01
So in this problem, we're given this family of curves here and asked to determine which one is f, f prime, f double prime, and since there's actually four of them here, we could say f triple prime, i suspect.
00:33
So let's look at it for a minute.
00:35
Remember that each time we do the derivatives, what we're doing? we're graphing the slope of the previous curve.
00:41
So the f prime is the slopes of the f curve.
00:47
And f double prime is the slope of the f prime curve.
00:54
And so on.
00:56
So let's see here for a minute.
00:58
If we just start out here with d for a second.
01:01
So let's look at the slope of what d is.
01:04
So first of all, the slope as we start up this curve is very positive, and it slows down and hits zero.
01:10
Right here.
01:13
Well, that's what this green line does.
01:16
And then the curve is negative.
01:18
The slope is negative all the way down until it hits the inflection point right here, which is where the slope would be zero, or be at its most, excuse me, at its most negative point.
01:33
And then it comes on down and slows down here.
01:38
So it approaches zero again.
01:40
Still negative, but approaches zero.
01:42
So that follows the green curve.
01:43
Doesn't it? and then the slope goes positive and gets greater and greater and greater, which is what this green curve does...