SOLUTION: A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 100ft of fence? W

You can put this solution on YOUR website!
Since 1 side is the barn, the farmer needs only 3 sides.There will
be 2 equal length sides perpendicular to the barn and one side parallel
to the barn.
Let = the length of a side perpendicular to barn
Let = the length of the side parallel to the barn
Let = the area enclosed by the fencing
Given:


--------------
formula for the area of a rectangle
And, from above,



This is a function . I can plot it and find the
maximum. I also know that, given a general equation
, there is a maximum if the sign of
is negative. That maximum occurs at
. In this case,




ft
When ,


ft


ft2
I'll plot the equation A(x), too

A good way to check to see if you have a maximum is
to just tweak the numbers a tiny bit, like

What's the area?
The area went down as it should
Then tweak the other way


area also went down
So, looks like a maximum