Inscribed rectangle.

[dat692]

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 2-x^2. What are the dimensions of such a rectangle with the greatest possible area?

 

[pka]

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 2-x^2. What are the dimensions of such a rectangle with the greatest possible area?

The area is \(\displaystyle A(x)=2x(2-x^2),~x>0\). Now maximize \(\displaystyle A(x)\)

 

[dat692]

more

width and height?

 

[HallsofIvy]

Have you drawn a picture? The wording of the original problem, together with pka's response should answer that for you but the graph will help you see it.