the area is, as always, length * height
Let the base be of size 2x, with its center at (0,0) and the corners at ±x
a = 2x(4-x^2)
da/dx = 8-6x^2
so the max area is 32/(3√3) when x=2/√3
Thus the rectangle's dimensions are 4/√3 by 8/3
A rectangle is inscribed with it's base on the x-axis and it's upper corners on the parabola y=4-x^2. What are the dimensions of such a rectangle with the greatest possible area?
Width=
Height=
1 answer