00:01
Here, we're given the graph of two functions.
00:04
And let's go ahead and label that this one is f, and this one, the red one, is g.
00:12
And we're given a third function, h of x.
00:15
We're told that that's f of x times g of x.
00:20
And we want to find h prime at different values.
00:24
So let's just find first h prime of x.
00:27
Well, what we're going to do here is say we have a product rule.
00:30
We have one function times another.
00:33
The product rule says take the derivative of the first, and you multiply by the second function unchanged.
00:41
Then you add the original function, f of x, unchanged, times the derivative of the second.
00:48
That's the product rule.
00:50
So if i want to find h prime of some values, say h prime of 1, well, i just need to plug those in.
00:58
So i need f prime of 1.
01:00
I need g of 1, and then i'll add that.
01:04
To f of one and g prime of one so now here's where our graph comes in what is f prime of one so let's go ahead and say h prime of one equals now the first part is f prime of one so here's one and f f prime is is just the slope of this line so you notice over the course of two i go up one two three so rise over run is three over two so f prime of one is three over 2.
01:40
Now it wants to know g of 1...