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. What is the rate of change of the area of a square with respect to its side length when

What Is The Rate Of Change Of The Area Of A Square With Respect To Its Side Length When class=

Sagot :

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.

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