A shopping mall manager creates a parabola to predict the number of shoppers in a mall, where z is the number of hours since 8 A.M. and y is the number of shoppers in the mall. Write a function f that models the number of shoppers in the mall over time. Then find the average rate of change in the number of shoppers over the interval in which the number of shoppers is increasing. Shoppers in Mall yA 500 400 (4, 320) 300 200 100 /(0, 0) (14, 0) 2 4 6 8 10 12 14 x Number of shoppers

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A:

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.