This is a little applet that lets you change the length of the one side to see how the area varies in the rectangular-bug-plots-area optimization problem we did in class 4/23.
The basic problem gives you 120 units of fencing to make a double rectangle.
From the diagram, we need 4x+3y units of fencing and get 2xy square units of area

Drag the X slider around and see what happens to the area of the rectangle.
What X gives you the biggest area?
What's the biggest possible area?
Does your answer match what we did in class?
What happens at the endpoints? (X certainly can't get smaller than 0 or bigger than 30.)