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A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 1-x^2. What are the dimensions of such a rectangle with the greatest possible area?

  • Calc -

    let the point of contact of the top right corner with the parabola be (x,y)
    then the base of the rectangle is 2x and its height is y
    Area = 2xy
    = 2x(1 - x^2)
    = 2x - 2x^3

    D(area)/dx = 2 = 6x^2
    = 0 for a max of area

    solve for x , then find y ...
    very easy from here on

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