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Math Help - Changing sides of a square (area and derivatives)

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    Changing sides of a square (area and derivatives)

    How fast are the sides of a square changing at the instant when its sides are 6 feet long and its area is decreasing at a rate of 2 square feet per second?

    I assume that the square is on a graph. Then I listed the known variables, which are:
    x=6
    y=6

    Since area is decreasing at a rate of 2 sq. ft/s, would x'=-2? Would I have to find the derivative of the formula Area =lw to help get the answer?
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    Quote Originally Posted by DarkestEvil View Post
    How fast are the sides of a square changing at the instant when its sides are 6 feet long and its area is decreasing at a rate of 2 square feet per second?

    I assume that the square is on a graph. Then I listed the known variables, which are:
    x=6
    y=6

    Since area is decreasing at a rate of 2 sq. ft/s, would x'=-2? Would I have to find the derivative of the formula Area =lw to help get the answer?
    The area formula for a square is

    A=s^2 taking the derivative you get

    \frac{dA}{dt} = 2s\frac{ds}{dt}
    plugging in the above info you get

    -2=2(6)\frac{ds}{dt} \iff \frac{ds}{dt} = -\frac{1}{6}
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