A rectangle is inscribed with its base on the x-axis and its upper corners of the parabola y= 9-x^2. What are the dimensions of such a rectangle with the greatest possible area?
The height is clearly going to be dependent on y, because the top corners touch the parabola. So what about the width? Well you need a way of expressing this length in terms of an x value. It's not simply x, because that doesn't cover the whole length of the base. Can you see the way to write the length of the whole base for a given that the bottom right corner is at (x,0)?