Question

The area of a square with side s is A(s)=s². What is the rate of change of the area of a square with respect to its side length when s=8?

Answer 1

Area of square is $A(s)=s^2.$

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

$\frac{dA}{ds}=2s.$

Note it is the same as A'. So,

$A'(s)=2s.$

Then, substitute the given value of s.

$A'(8)=2(8)=16.$

Answer:

The rate of change of area with respect to $s$ when $s=8$ is 16.