What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y equals 27 minus x^2?

Answer 1

if the base has width 2x, then the area is

a = 2xy = 2x(27-x^2) = 54x - 2x^3
da/dx = 54 - 6x^2 = 6(9-x^2)
da/dx=0 when x=3

So, the rectangle is 6 by 18 with area=108