When S is sales and t is time, and the original function is S(t), what does S'(24)>0 and S''(24)<0 represent?
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When S is sales and t is time, S'(t) is the selling or sales rate (number of items sold in a particular period of time).

S(t) is a function which is a model of how many items are sold in a varying period of time (t). The first derivative S'(t) gives the sales rate. S''(t) is the rate of change of the selling rate. For example, in a year, the sales rate may depend on the season. Perhaps it's the sale of holiday or summer clothing. The sales rate may be low in certain months. t might be the number of months from the beginning of a year. During cold months the sales rate might be low, but as the weather gets warmer, sales increase (this is acceleration given by S''(t), the second derivative) and then as the weather gets cooler, sales decrease (this is deceleration or negative acceleration).

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