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. 

Answer 2

The solution according to the given question is provided below in the explanation segment.

According to the question,

The cost of drilling x feet is:

$c(x) = f(x) \ dollars$

(a) $f'(x) = \frac{df(x)}{dx} \ \frac{dollars}{feet}$

(b) Throughout the practical terms,

$f'(x)$ represents how many dollars its going to cost one feet.

(c) $f'(x)$ is positive,

The cost of drilling increases as "x" feet increases.

(d) The cost of drilling an additional foot at 300 feet will be $f'(x) \Delta \ x$

here,

• $\Delta x =0$
• $f'(300) =1000$

then,

= $1000\times 1$

= $1000 \ dollars$

If you want drill 1 more feet at 300 feet, its going to cost 100 dollars in one.

Thus the above answer is correct.              

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