Given a circle, prove that the square is the rectangle of maximal area that can be inscribed in the circle.
Proof. Let and
denote the lengths of the sides of the inscribed rectangle, and
denote the radius of the circle. Then
implies
. Therefore,
We then have when
and
Hence, has a maximum at
. By our equation for
we then have
Thus, , so the rectangle is a square
The analysis of f'(x) is incorrect, despite the fact of the answer being correct.
your radius is 2r, instead of r.