Without calculus, I am trying to find the maximum area of a rectangle that is bounded by the $x$ and $y$ axis and bounded by the line $y=-2x+1$. It is also parallel to both axis.
I would post an attempt but I am lost on how to even get this started...
Area = $xy$ $$ = x(-2x+1)$$ $$ = -2x^2+ 2x$$
This parabola opens down so it has a maximum at its vertex which is $(1/4, 3/8)$