Final answer:
The height of the rectangle, whose area is a maximum when it is inscribed under the graph of y=8−x^2, is 8.
Step-by-step explanation:
To find the height of the rectangle, we need to first determine the values of x for which the area of the rectangle is maximized. In this case, the base of the rectangle is on the x-axis, so the height will be the difference between the y-values of the curve y = 8 - x^2 at the two x-values that define the base.
The maximum area of the rectangle will occur when the base spans the entire width of the curve, which is from x = -∞ to x = ∞. To find the height, we evaluate the curve at the two x-values: y = 8 - (-∞)^2 = 8, and y = 8 - (∞)^2 = -∞. Therefore, the height of the rectangle is 8 - (-∞) = 8.