# Changing sides of a square (area and derivatives)

• Oct 13th 2009, 05:38 PM
DarkestEvil
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:
$\displaystyle x=6$
$\displaystyle y=6$

Since area is decreasing at a rate of 2 sq. ft/s, would $\displaystyle x'=-2$? Would I have to find the derivative of the formula Area$\displaystyle =lw$ to help get the answer?
• Oct 13th 2009, 08:36 PM
TheEmptySet
Quote:

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:
$\displaystyle x=6$
$\displaystyle y=6$

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

The area formula for a square is

$\displaystyle A=s^2$ taking the derivative you get

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

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