2019 THREE(c)

A rectangle has one vertex at $(0,0)$, and the opposite vertex on the curve $y=4-\sqrt{x}$, where
$0<x<16$, as shown on the graph below.

Find the maximum possible area of the rectangle.

*You must use calculus and show any derivatives that you need to find when solving this
problem.*

*You do not need to prove that the area you have found is a maximum.*