posted by Anonymous .
A rectangle with its base on the x-axis is to be inscribed under the graph of y=2-x^2. Find the height of the rectangle if the area is the largest possible area.
let the point of contact of the rectangle with the parabola in the first quadrant be P(x,y)
So the base of the rectangle is 2x and its height is y
Area = 2xy
= 4x = 2x^3
d(Area)/dx = 4 - 6x^2 = 0 for a max/min of area
6x^2 = 4
x = √(2/3)
then the height for a max area
= 2 - 2/3