Using derivatives, it is found that the correct option is given by:
A. The expression 2x² + 20x + 32 represents the average rate of increase in the total number of clubs in the network across all states.
What is the meaning of the derivative of a function?
It is the rate of change of the function over a period of time.
In this problem, the total number of people in the book club after x months is given by:
f(x) = 2x³ + 20x² + 64x + 64
The derivative is given by:
f'(x) = 4x² + 40x + 64 = 2(2x² + 20x² + 32).
It represents the average rate of change across all states, hence option A is correct.
More can be learned about derivatives at https://brainly.com/question/2256078
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