00:01
For absolute extrema like this, we're doing the extreme value theorem and the function is 4 cosine of t.
00:11
Now we're doing that from negative 3 pi over 2 to positive 3 pi over 2.
00:18
And what i need to do is take the derivative of this function, which shouldn't be too bad.
00:22
The derivative of cosine is negative sine, just that that 4 is there as part of the problem.
00:28
And where does sine equal zero then? well, if you're familiar with the unit circle, sine equals zero at the beginning at that ordered pair sine is the y -coordinate.
00:41
So at zero, but i also have to go clockwise to get to negative pi, but also counterclockwise, which is positive pi.
00:50
And at this point, what you can do is you can just test out the endpoints, like f of negative 3 pi over 2, f of negative pi, f of zero.
01:09
There's going to be a lot of repeat answers here, f of pi, as well as the other endpoint f of 3 pi over 2.
01:16
And i'm just going back and just plugging into f.
01:20
So as i plugged in negative 3 pi over 2, which is up here at zero one, well, cosine is zero...