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March 30, 2017

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Hello, could someone please help me with this problem? I'm a little stuck with it. Thanks, Isaac

A rectangle is to be inscribed with its base on the x-axis and its other two vertices above the x-axis on the parabola y=9-x^2

(a) find the dimensions of the rectangle of largest area.

(b) Find the area of the largest rectangle.

  • Calculus - ,

    Since the parabola is symmetric about the line x=0, let the rectangle have corners

    (-x,0) (x,0) (x,y) (-x,y)

    Since y is 9-x^2, the rectangle is

    2x by (9-x^2) in width and height. The area is thus

    A = 2x(9-x^2) = 18x - 2x^3

    To find the value of x which gives maximum area, we want

    A' = 0
    A' = 18 - 6x^2
    A' = 0 when x = √3

    So, the rectangle is

    2√3 by 6 with area 12√3

  • Calculus - ,

    where does the 6 come from

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