00:01
When you're given f of x is equal to sine of 9x, i'm interpreting this to be times cosine of 9x.
00:09
What you need to do is take the derivative of this for the critical points.
00:15
So i'm interpreting points to be x and y coordinates.
00:19
So the first thing is to take the derivative.
00:21
And i'm doing the product rule where the derivative of sine is cosine.
00:26
You leave the 9x alone, and the derivative of 9x is 9.
00:30
I'm leaving this other piece alone.
00:34
I'm just going to write s squared.
00:35
And part of the product rule is to add to it, except the derivative of cosine is negative sine.
00:43
You leave that 9x alone.
00:45
The derivative of the inside is 9.
00:49
And you leave this other piece alone, so it becomes squared.
00:52
So at this point, i think what i would do is factor out a negative 9.
00:58
Actually, just make it positive 9.
01:00
And then we're looking at cosine squared of 9x minus sine squared of 9x.
01:07
And what we need to see is where the derivative will equal 0.
01:12
And really, the only place that will equal 0 is if cosine squared of 9x equals sine squared of 9x.
01:22
And what we're looking for then is basically on the unit circle where this cosine equals sine is at the ordered pair root 2 over 2 root 2 over 2, which is pi over 4 radians...