Chapter 4.2, Problem 9E

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

$C\left(x\right)=20+4,000x+0.05x^2.$

a. Find the marginal cost function, and use it to estimate how fast the cost is increasing when $x=4$. Compare this with the exact cost of airing the fifth commercial. [HINT: See Example 1.]

b. Find the average cost function $\bar{C}$, and evaluate $\bar{C}\left(4\right)$. What does the answer tell you? [HINT: See Example 2.]