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calculus

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1.Ruth has 240 feet of fencing available to enclose a rectangular field. Express the area A of the rectangular field as a function x, where x is the length of the field.

2. For what value of x is the area largest?

3. What is the maximum area?

  • calculus -

    let the length be x
    let the width be w
    but 2x + 2w = 240
    x + w = 120
    w = 120-x

    area = xw = x(120-x)
    = -x^2 + 120x

    d(area)/dx = -2x + 120
    = 0 for a max of area
    -2x = -120
    x = 60
    then w = 120-60 = 60

    for the max area the rectangle should be a square of 60 ft by 60 ft
    for a max area of 3600 ft^2

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