# Optimization and maximum area of a rectangular enclosure

1. Nov 19, 2004

### TSN79

I've used differentiation to find that a rectangular enclosure made up of a 100m fence should have four sides all 25m to be as large as possible. The function I get is $$50x-x^2$$. As I said, differentiating this function gives me the largest area possible. But how would I go about finding how long the sides must be in order to make the area as small as possible...?

2. Nov 19, 2004

### vsage

the maximized area was found at the maximum value of x (which happened to fall on the local maximum) so it makes sense the minimized area would be found at a value of x at the absolute minimum on the acceptable domain. Just be sure to keep within the constraints of what the perimeter is.