If a rectangle has a fixed perimeter, find for what dimensions the rectangle will have maximum area.[br][list][br][*]Change the shape of the rectangle by moving the blue point.[br][/*][*]The red point in the first quadrant has an [math]x[/math]-coordinate equal to the blue side of the rectangle and a [math]y[/math]-coordinate equal to the area of the rectangle. Observe the way the point is moving to find when the rectangle will have maximum area.[/*][*]Enter the function that will describe the area as a function of the blue side ([math]x[/math]) of the rectangle. [br][br][/*][/list]