The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. Here is a possible model:

The daily cost in dollars to reduce emissions by q pounds of pollutant in a day is given by

C$($q$)=4,400+97$q$2.$

$($a$)$ What is the average daily cost per pound when emissions are reduced by q pounds in a day?

C$($q$)=$

Incorrect: Your answer is incorrect.

$($b$)$ What level of reduction corresponds to the lowest average daily cost per pound of pollutant? $($Round your answer to two decimal places.$)$

Incorrect: Your answer is incorrect.

pounds of pollutant

What would be the resulting minimum average daily cost per pound? $($round to the nearest dollar$)$

Incorrect: Your answer is incorrect.

dollars

Second derivative test:

Your answer above is a critical point for the average daily cost function. To show it is a minimum, calculate the second derivative of the average daily cost function.

C$"($q$)=$

Incorrect: Your answer is incorrect.

Evaluate

C$"($q$)$

at your critical point. The result is

$---$Select$---$

Incorrect: Your answer is incorrect.

$,$ which means that the average cost is

$---$Select$---$

Incorrect: Your answer is incorrect.

at the critical point, and the critical point is a minimum.