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. (Round to the nearest hundreth)

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  1. Let the point of contact of the rectangle in the first quadrant be (x,y)

    then the base of the rectangle 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
    x = ±2/6
    then height = y = 2 - 4/6 = 4/3
    = 1.33 to the nearest hundreth

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