Question

suppose that the cost of drilling $x$ feet for an oil well is $c = f(x)$ dollars.
a. what are the units of $f(x)$? (write each word in its entirety, in lower case).
units:

b. if youve already drilled 340 feet, estimate the cost of drilling an additional foot if $f(340)=1000$.
cost: dollars

Explanation:

Step1: Recall derivative unit concept

The derivative $f^{\prime}(x)$ is the rate - of - change of $y = f(x)$ with respect to $x$. Here, $y$ is cost $C$ in dollars and $x$ is the depth of drilling in feet. So the units of $f^{\prime}(x)$ are dollars per foot.

Step2: Interpret the value of the derivative

The value of $f^{\prime}(340)$ represents the approximate cost of drilling an additional foot when $x = 340$ feet. Given $f^{\prime}(340)=1000$, the cost of drilling an additional foot is 1000 dollars.

Answer:

a. dollars / foot
b. 1000