Find the dimensions that give the largest area for the rectangle shown in the figure.
9
The x y-coordinate plane is given. A curve and a rectangle are given.
The curve labeled y = 9 − x2 enters the window in the third quadrant, goes up and right becoming less steep, crosses the negative x-axis, changes direction at a point on the positive y-axis, goes down and right becoming less steep, passes through the point (x, y), crosses the positive x-axis, and exits the window in the fourth quadrant.
The rectangle has its base on the x-axis and is centered on the positive y-axis.
The top right corner of the rectangle touches the curve at the point (x, y).
Its base is on the x-axis and its other two vertices are above the x-axis, lying on the parabola
y = 9 − x2.
(Round your answers to two decimal places.)