The owner of a cattle ranch would like to fence in a rectangular area of 3 m^2 and then divide it in half with a fence down the middle. what is the minimum amount of fencing that the rancher must use?

If you notice the picture below, the amount of fencing, or perimeter, that will be used will be 3w + 2l

now    

solve for "w", to see what critical points you get, and then run a first-derivative test on them, for the minimum

notice the    so.  you can pretty much skip that one, though is a valid critical point, the width can't clearly be 0

so.. check the critical points on the other