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1. The cost, in thousands of dollars, of airing x television commercials during a Super Bowl game is given by

C(x) = 150 + 2280x 0.02x².

(a) Find the marginal cost function C'(x). HINT [See Example 1.]

C'(x)

=

Use it to determine how fast the cost is increasing when x = 4. thousands of dollars Compare this with the exact cost of airing the fifth commercial.

The cost is going up at the rate of $ per television commercial. The exact cost of airing the fifth commercial is $ . Thus, there is a difference of $ .

(b) Find the average cost function

C,

and evaluate

C(4).

HINT [See Example 4.]

C(x)	=
C(4)	=	thousands of dollars

What does the answer tell you?

The average cost of airing the first four commercials is $ per commercial.

2. Your college newspaper, The Collegiate Investigator, sells for 90 per copy. The cost of producing x copies of an edition is given by

C(x) = 20 + 0.10x + 0.001x² dollars.

(a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.]

R'(x)	=
P'(x)	=

(b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition.

revenue	$
profit	$
marginal revenue	$	per additional copy
marginal profit	$	per additional copy

Interpret the results.

The approximate ---Select--- profit loss from the sale of the 501st copy is $ .

(c) For which value of x is the marginal profit zero? x = copies Interpret your answer.

The graph of the profit function is a parabola with a vertex at x = , so the profit is at a maximum when you produce and sell copies.

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