Question

Suppose that the cost of drilling x feet for an oil well is C=f(x) dollars. a) What are the units of f'(x)? b) In practical terms, what does f'(x) mean in this case? c) What can you say about the sign of f'(x)? d)Estimate the cost of drilling an additional foot, starting at a depth of 300 ft, given that f'(300)=1000.

Answer 1

A. The term "units" refers to the measurements in the original question or problem. When looking at the question, the units we are measuring are dollars/feet. 
B. In this case, the f'(x) means we are looking for the cost (in dollars) to drill the next foot down. 
C. Since the cost increases the more feet we drill down, the sign of f'(x) is positive.