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?

width=

height=

The area of a rectangle is given by A = length * width.

width of the given rectangle is x

height is y = 2 - x^2

Area = x (2 - x^2) = 2x - x^3

For area to be maximum, dA/dx = 0

dA/dx = 2 - 3x^2 = 0

3x^2 = 2

x^2 = 2/3

x = √ (2/3)

y = 2 - (√ (2/3)) ² = 2 - 2/3 = 4/3

Therefore, the required rectangle has a width of 2√ (2/3) ≈ 1.63 and a height of 4/3 ≈ 1.33