00:01
Suppose a rectangle with minimum perimeter has an area of 441 square feet.
00:06
Now to determine this perimeter, we first want to define our objective function, which in this case is the function that's being minimized, the perimeter function.
00:18
Now, the perimeter, p of a rectangle, is equal to twice the sum of the length and its width.
00:25
But since b is written in terms of two variables, we have to rewrite this so that it will be written in terms of one variable only.
00:34
We will use the fact that the area of this rectangle is 441 square feet.
00:41
So if the area of the rectangle is length times the width, and this is equal to 441, then our length, l is equal to 441 all over dollar.
00:56
Substituting this to our objective function, our p now is equal to twice 441 over w plus w.
01:08
Now that we've written the objective function in terms of one variable, the next step will be to take the derivative of p.
01:15
Differentating p with respect to w, we have p prime equal to twice, negative 441 over w squared plus, 1...