00:07
So this problem, you've got a piece of paper that is four meters by four meters.
00:17
What you're going to do is to cut congruent squares out of the corners, fold this up, and you want to maximize the volume of the box that you get.
00:30
So what we don't know is how much each of these little corners is going to be.
00:39
Okay? but i do know that this is going to be this side is 4 minus 2x.
00:45
This side right here is 4 minus 2x.
00:49
Then when i fold this up and get a box, so when i get a box, and this is where i'm not so great at drawing this guy, you're going to get 4 minus 2x, 4 minus 2x, and the height of that box is going to be x.
01:05
So the expression for the volume here, the volume of this box is going to be 4 minus 2x, 4 minus 2x times x.
01:21
So this is going to be the volume is equal to 16 minus 16x plus 4x squared times x.
01:33
The expression for the volume is going to be a cubic.
01:36
4x cubed minus 16 x squared plus 16.
01:44
Now, let's differentiate this.
01:47
So, dvdx is going to be equal to 12x squared minus 32x.
02:01
Scarabit this, and this had an x on here, plus 16.
02:07
So this is, if i factor this out, these are all divisible by four.
02:15
So 3x squared minus 8x plus 4...