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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.

  • calculus -

    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
    = 2x(2-x^2)
    = 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
    = 4/3

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