Chapter 2.2, Problem 41ES

Suppose that the cost of drilling $x$ feet for an oil well is $C=f\left(x\right)$ dollars.

(a) What are the units of $f^{\prime }\left(x\right)$ ?

(b) In practical terms, what does $f^{\prime }\left(x\right)$ mean in this case?

(c) What can you say about the sign of $f^{\prime }\left(x\right)$ ?

(d) Estimate the cost of drilling an additional foot, starting at a depth of $300\text{ ft}$ , given that $f^{\prime }\left(300\right)=1000$ .