Changing sides of a square (area and derivatives)

**DarkestEvil** · October 13th 2009, 05:38 PM

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?

**TheEmptySet** · October 13th 2009, 08:36 PM

Originally Posted by DarkestEvil

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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