Question

The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 20 + 4,000x + 0.05x2. (a) Find the marginal cost function C'(x). HINT [See Example 1.] C'(x) = Use it to estimate how fast the cost is increasing when x = 4. thousand 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 2.] C(x) = C(4) = thousand dollars What does the answer tell you? The average cost of airing the first four commercials is $ per commercial.

          The cost, in thousands of dollars, of
airing x television commercials during a sports
event is given by
C(x) = 20 + 4,000x + 0.05x2.
(a) Find the marginal cost function
C'(x).
HINT [See Example 1.]
C'(x) =
Use it to estimate how fast the cost is increasing when
x = 4.
thousand 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 2.]
C(x) =
C(4) =
thousand dollars
What does the answer tell you?
The average cost of airing the first four commercials is $
per commercial.

Added by Willie J.

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