It's been a while since I last tackled high-school math, and a friend asked me this question which I can't remember how to approach.
I have the following: $ y = -x^2 + 5x $ Which produces an inverse parabola, intersecting with the $x$ axis on $(0,0)$ and $(5,0)$ (I still remember that much).
The question is, place a point $a$ on the parabola graph, which will produce the largest perimeter rectangle with the axes.
Image
The point is to find the $a$ where $P_{aboc}$ is the largest.
I would appreciate if anyone could point me to the right direction, even if not directly giving the solution!
Thanks in advance!