00:01
Okay, so we have this function, f of x, is 4 minus x cubed.
00:08
And it's continuous, and it's defined on this closed interval from 2 to 1, negative 2 to 1.
00:16
And so we know about the extreme value theorem.
00:18
We have an absolute maximum and absolute minimum.
00:21
And those will occur either at a critical point or at the endpoints of the interval.
00:27
So let's find our critical points first.
00:29
So we take the derivative.
00:33
And so when does the derivative equal 0? well, that happens when x is zero.
00:41
So we have a critical point.
00:45
X equals zero.
00:46
And so we need to test the value of the function at zero, the left end point, and the right end point.
00:51
So f of negative 2 is 4 minus negative 8...