Solution:
Given:
[tex]A(s)=s^2[/tex]
To get the rate of change of the area of a square with respect to its side, we differentiate the area with respect to the side.
Hence,
[tex]\begin{gathered} A(s)=s^2 \\ \frac{dA}{ds}=2s \\ \\ \text{Hence, the rate of change is 2s} \end{gathered}[/tex]
Hence, when s = 6, the rate of change is;
[tex]\begin{gathered} \frac{dA}{ds}=2s=2\times6 \\ \frac{dA}{ds}=12 \end{gathered}[/tex]
Therefore, the rate of change of the area of a square with respect to its side length when s=6 is 12.
