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 byqpounds of pollutant in a day is given by

C(q) =4,900+90q².

(a) What is the average daily cost per pound when emissions are reduced byqpounds in a day?

C(q)=

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

pounds of pollutant

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

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)=

EvaluateC"(q)

at your critical point. The result is

---Select---

positive

negative

, which means that the average cost is

---Select---

concave up

concave down

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