6. The base of a rectangle lies along the x axis, and the upper two vertices are on the curve defined by y = kx - x^2. Determine the dimensions of the rectangle with the maximum area.
I started off with setting up the formula and the constraint . After subbing into , I found the derivative of and solved for , which turned out to be . I then subbed into , which gave me a value of , and subsequently I found the maximum area to be .
The problem is that after I double checked my diagram, I found that it was inconsistent with the actual equation. Namely, it did not account for the fact that when x = 0, y = 0, and thus it had a large gap in the center.
So my question is this: Did I set up my equations correctly? Is my parabola supposed to look something like http://jwilson.coe.uga.edu/emt668/EM...s/image007.jpg or something like http://xsquared.wikispaces.com/file/...l_parabola.jpg (but moved to the right a bit more)?