a. The meaning $f'(x)$ is the rate of change of the production cost; dollars/ounce. b. Increases to $17$ dollars/ounce. c. Short term: decrease; long term: increase
Work Step by Step
a. The meaning $f'(x)$ is the rate of change of the production cost with respect to the number of ounces of gold. The unit is dollars/ounce. b. The value of $f'(800) = 17$ means that after $800$ ounces of produced gold, then the rate/cost of production increases to $17$ dollars/ounce. c. The short term $f'(x)$ could decrease due to the amount of gold deposits the mine has. However, in the long term it would cost more to extract the gold deposits, so the $f'(x)$ will increase.