Barrons AP Calculus

78. (E) Center the ellipse at the origin and let (x, y) be the coordinates of the
    vertex of the inscribed rectangle in the first quadrant, as shown in the
    figure.

To   maximize    the     rectangle’s     area   A    =   4xy,    solve   the     equation    of  the

ellipse,    getting

So   .  Graph       in  the window  [0,5]   ×   [0,150].

The calculator  shows   that    the maximum area    (the    y-coordinate)   equals

100.