optimization question

Question

Find the maximum area of a rectangle inscribed in the region bounded by the graph of y= 4-x / 2+x and the coordinate axes

Answer 1

I'm not going to write all of this down, but since y = (4-x)/(x+2), and xy is the area, taking the derivative of this product and setting to 0 yields x = 2 and y = 0,5, so the Area = xy = 1. But then I graphed it and noticed that when x=1, y=1 so that Area = 1 also.