00:01
Here we're given that f of x is equal to the sign of 4x.
00:06
And we want to find the absolute maximum on the region from negative pi over 4 to pi over 4.
00:13
What we have to do now is find the critical points, which is where the derivative is zero, and then just figure out which is bigger or smaller at the critical points in the endpoints.
00:23
So i'm going to say f prime of x is equal to 4 times the cosine of 4x, since that's the derivative of sign.
00:33
And i set that equal to zero.
00:35
The four goes away, so i get cosine of 4x equals 0, or 4x is equal to whenever cosine is equal to 0.
00:44
Now, cosine is equal to 0 at pi over 2 and negative pi over 2, and so on and so forth.
00:53
So that means that x will be divide each of those by 4, so i get pi over 8 and negative pi over 8.
01:06
And so i have two critical points.
01:09
So let's just find out what is the function value at each of those points...