The area of a square with sides of length s is given by `A = s^2` .   Find the rate of change of the area with respect to s when s = 4 meters.Find the rate of change of the area with respect to s...

The area of a square with sides of length s is given by `A = s^2` .  

Find the rate of change of the area with respect to s when s = 4 meters.

Find the rate of change of the area with respect to s when s = 4 meters.

A'(4) = m2/m

A'(4) =   ?  m2/m

Asked on by david3

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lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

The area of square is:

`A=s^2`

To determine the rate change of its area with respect s, take the derivate of  A.

`d/(ds)A=2s`

Note that `(dA)/(ds)` is the same as A'. So,

`A'=2s`

Then, substitute the given value of s.

A'(4)=2(4)=8

Hence, when s=4m, the rate of change of area with respect to s is `8` `m^2/m` .

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