00:01
I already have a fence on here.
00:03
And i'm going to assume it's long enough that we're good, that we don't have to worry about fixing anything or anything like that.
00:10
So these two side lengths will be x, and this side length will be y.
00:15
So all i know is that the area of a rectangle is x times y, and they tell you you have 30 ,246 square feet.
00:25
Now, i'm going to use that.
00:27
But what we also know is that the perimeter of this that we have to purchase is 2x plus y, but not only 2x plus y, but we also have to acknowledge that the side lengths of 2x cost $6.
00:44
So it's like a cost equation, and then $18 times y for that length.
00:52
So we want to minimize cost.
00:59
And how do you minimize cost is by finding the derivative? well, what i need to do first is go back and figure out either what y or x is.
01:07
And it really doesn't matter which one you do.
01:10
Maybe just do y equals 30 ,246 divided by x.
01:16
So you can actually take your cost equation of 12x.
01:20
Let's see, what's 18 times? that's a big number.
01:26
Times 30246, 54 ,544 ,428.
01:34
And instead of writing divided by x, my right is x to the negative first power.
01:38
Because when you minimize something, you have to take the derivative, so it would be 12, and then the power rule.
01:45
So 544, 428, and you subtract one from your exponent and set it equal to 0.
01:54
Remember that that means divided by x squared.
01:58
So i'm going to add that number to the other side.
02:04
So i'm now going to multiply x squared over...