00:01
All right, so we're given the following graph, a of x equals 0 to x, the integral from 0 to x of f of x dt, where f of x is shown in the graph below.
00:18
We're going to determine where a of x has a local max.
00:22
What we're going to note here is that if we find the derivative of a, that gives us the function f of x.
00:29
So the graph of f of x below is actually the derivative of a.
00:34
So let's just think of it as the derivative of a, not as the function a, as the derivative.
00:39
So if this graph that we're given, which looks like this, is going to be the derivative of a, and we're given that the x -axis, it's something like this.
00:50
That's the x -axis, and then this is going to be the y right about here.
00:55
In order for us to have a local min or local max, i have to have a negative to a positive derivative to have a local min, and then a positive to a negative derivative to have a local max.
01:09
In order for this to be the case, i'm going to highlight where a prime, or the derivative of f, or in this case, a, is positive.
01:18
It's positive here, and it's positive here.
01:22
I'm now going to highlight where it's negative.
01:25
Negative there, negative there, negative there.
01:28
Wherever we go from a blue to a yellow, blue to a yellow indicates a negative to a positive...