Final answer:
The rate of change of the area of a square with a side length of 12 units is 24 square units per unit increase in side length. This is calculated using the derivative of the area function A(s) = s² which is 2s.
Step-by-step explanation:
The question asks about the rate of change of the area of a square with respect to its side length at a particular side length, specifically when s=12. To find this rate of change, we need to take the derivative of the area function A(s) = s² with respect to s. The derivative of s² with respect to s is 2s. Therefore, when s=12, the rate of change of the area is 2×12 = 24. This value means that for a small increase in the side length of the square from 12 units, the area would increase approximately by 24 square units.