A rectangle has one corner on the graph of y=f(x)=33-3x^2, another at the origin, a third on the positive y-axis, and the fourth on the positive x-axis. Express the area, A, of the rectangle as a function of x=2

Answer 1

Let the rectangle have width x and height y=33-3x^2

clearly the area is

a = xy = x(33-x^2)