algebra

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 27 - x2

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  1. Did you make a sketch ?

    let the vertex in quadrant I be (x,y)
    then the vertex in quadratnt II is (-x,y)

    the base of our rectange = 2x
    and the height is y

    Area = xy
    = x(27 - x^2)
    = -x^3 + 27x
    d(area)/dx = 3x^2 - 27
    = 0 for a max of area

    3x^2 = 27
    x^2 = 9
    x = ±3
    y = 27-9 = 18

    largest area = 3(18) = 54 square units

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