Correcting a Prediction The financial analysts at the store in Example 5 corrected their p...

Correcting a Prediction The financial analysts at the store in Example 5 corrected their projections and are now expecting the total sales for the x day of January to be

thousand dollars.

(a) Let S(x) be as in Example. Compute T (1), T ′(1), S(1), and S′(1).

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(b) Compare and interpret the data in part (a) as they pertain to the sales on January 1.

Example

DEFINITION Marginal Cost If C(x) is a cost function, then the marginal cost function is C′(x). The marginal cost of producing a units, C′(a), is approximately equal to C(a + 1) − C(a), which is the additional cost that is incurred when the production level is increased by 1 unit from a to a + 1.

Before we give an example, let us note that if C(x) is measured in dollars, where x is the number of items, then C′(x), being a rate of change, is measured in dollars per item.