00:01
Here, we're given the graph of two functions, f, which is in black and g, which is in red.
00:08
And we're also told that there's a third function, h of x, which is equal to f of x times g of x.
00:15
And we're asked for some details about the derivative of h.
00:18
So let's go ahead and calculate that derivative.
00:21
It's going to be a product rule, because we just have one thing times another.
00:24
Product rule says you take the derivative of the first times the second unchanged, plus the first, unchanged times the derivative of the second.
00:35
So now if we want to evaluate this at a point, say h prime of 1, that just means plug in that 1.
00:44
So we have h prime of 1 times g of 1 plus f of 1 times g prime of 1.
00:51
And we do the same thing at any other point.
00:53
Say 2, we would get h prime of 2 is equal to f prime of 2 times g of 2 plus gf of 2 times g prime of 2.
01:01
But now h prime of 1, equals f prime of 1.
01:05
Well, what is f prime of 1? that's going to be the slope at this point.
01:13
Well, the slope of this graph, if i go from here to here, that's a change of two values in the y direction, and two for x...