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)?