Math Is Fun Forum

freddogtgj

Member

Registered: 2006-12-02

Posts: 54

Differentiation Problem

Hi all,

I need help answering a question that I am having trouble with.  I think it has to do with differentiation, but not too sure.

Question

A farmer wants to put up a fence around a rectangular pen with an area of 128m^2.

One side of the rectangle is a wall, what is the least length of fence needed to cover the perimeter left?

I hope I covered everything in the question.
Thanks in advance!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Differentiation Problem

Hi freddogtgj;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Cosmopolite

Member

Registered: 2011-01-04

Posts: 6

Re: Differentiation Problem

Hey bobbym

I read your answer but I don't understand the part where you differentiate with respect to W. Would you explain to me why you did that? Thank you.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Differentiation Problem

Because of this equation here.

P is a function of w. Like the familiar y is usually written as a function of x. You can write that as:

I set it up like that because we are looking for the rate of change of W. Could have picked L also. To get the minima we are looking for where the rate of change is 0 ( level with the x axis ). So we differentiate in terms of W and set that derivative to 0. This is how we go about finding extrema. Remember minimizing the sides is how you minimize the perimeter.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Cosmopolite

Member

Registered: 2011-01-04

Posts: 6

Re: Differentiation Problem

Thank you.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Differentiation Problem

Hi Cosmopolite;

Your welcome glad to help.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.