Question

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=5-x^2. What are the dimensions of such a rectangle with the greatest possible area?

Answer 1

If the lower corners are at (x,0) and (-x,0), then the upper corners are at (x, x^2 - 5) and (-x, x^2 - 5).

Answer 2

The area A is 2x(-x^2 + 5) = 2x^3 - 10x. Set the derivative equal to 0 and solve for x:
6x^2 - 10 = 0
x = sqrt(5/3)
A = 10 sqrt(15)/9.