Here is the problem:
A rectangle has its base on the $x$-axis and its upper two vertices on the parabola $y=12-x^2$ What is the largest area the rectangle can have, and what are its dimensions?
Well, I don't really know where to start. My initial idea was to find inflection points because I figured that is where the vertices would be, but there are no inflection points because it is a parabola.
Then I though about finding where the derivative and the parabola cross, found it, but I don't know how that will help me.
I really don't know where to start.
Any help is appreciated, thanks.