# Homework Help: Maximum Area Problem

1. Oct 30, 2009

### 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 cant even being to attempt it.

2. Oct 30, 2009

### 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

3. Oct 30, 2009

### Cstreet09

So does that mean L=400-w?

4. Nov 3, 2009

### LCKurtz

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

5. Nov 4, 2009

### 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?

6. Nov 4, 2009

### HallsofIvy

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

7. Nov 4, 2009

### Staff: Mentor

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

8. Nov 8, 2009

### tiny-tim

He probably means light-years!

9. Nov 8, 2009

### Staff: Mentor

As opposed to heavy years?

10. Nov 9, 2009

### Kaimyn

Nah, I would have thought dark years

11. Nov 9, 2009

### 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.