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A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 8−x2. What are the dimensions of such a rectangle with the greatest possible area?
width=
length=

  • calc -

    if the rectangle extends from -x to x,

    a = 2xy = 2x(8-x^2)
    da/dx = 16 - 6x^2
    a has a max at x = 4/√6

    width = 8/√3
    height = 16/3

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