*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)?