Max Area Problem: Find Rectangle w/ Largest Area (400 yrs Fencing)

[Cstreet09]

1. David has 400 yrs of fencing and wishes to enclose a rectangular area. a) express the area A of the rectangle as a function of the width w of the rectangle. b) For what value of w is the area largest. c) What is the maximum area?



2. A=xy... My teacher does not want us to use derivatives.



3. I can't even being to attempt it.

 

[ideasrule]

You got A=Lw and you want the area in terms of w, so the next step is to figure out what L is (in terms of w) and sub it into A=Lw.

Hint: use the perimeter formula

 

[Cstreet09]

So does that mean L=400-w?

 

[LCKurtz]

So does that mean L=400-w?

No. Draw a picture and label all 4 sides L or w. What is it that equals 400?

 

[Kaimyn]

It may help to think of it this way:

What is greater?

(x-n)(x+n)
or
x²

To help, what is another way of writing the first one?


What's to say you can't use optimisation (derivatives) to check your answer?

 

[HallsofIvy]

There would be no reason to use derivatives. The function to be optimized is a quadratic and completing the square works nicely.

 

[Mark44]

David has 400 yrs of fencing

That's going to take him a very long time!

 

[tiny-tim]

He probably means light-years! ​

 

[Mark44]

As opposed to heavy years?

 

[Kaimyn]

Nah, I would have thought dark years

 

[tiny-tim]

ah … dark time …

that mysterious phenomenon which is generally interspersed among ordinary time, but occasionally is more concentrated, causing effective time to pass more slowly and more heavily.