Question

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=2–x2. What are the dimensions of such a rectangle with the greatest possible area?

I got Width = 4/1.732 but i don't know why its wrong

I got Height = 4/3 which is right

Answer 1

I assume your equation is y = 2-x^2

The the contact point of the rectangle with the curve be (x,y) in the first quadrant
so the base is 2x, and the height is y
Area = 2xy
= 2x(2-x^2)
= 4x - 2x^3
d(Area)/dx = 4 - 6x^2 = 0 for a max of Area
6x^2 = 4
x^2 = 4/6 = 2/3
x = .8165
so the base is 2x = 1.633
and the height is 2 - (.8165^2 = 1.3333