Disclaimer, I'm in pre-ap algebra 2, not calc lol. But based on common knowledge + a quick google search, I'm fairly certain this is the right answer.
So, first you need to find how many gallons the car uses per year.
Since x is the number of gallons, this would be 15000/x.
Now, you need to multiply however many gallons the car used by 2.95 to get the cost, C.
C=2.95(15000/x) is your function for this problem.
However, this can also be written as C=[tex] \frac{44250}{x} [/tex].
Let's fill in the row for C first.
Starting with 10 mpg.
44250/10
4425
So the first value should be 4425. Keep on doing this for the rest.
Now for dC/dx, this means rate of change in C caused by a change of the value x.
Starting with 10 mpg.
-4425/10
-442.5
So in the end, the table should look like this (approximating to decimals)
[tex] \left[\begin{array}{cccccccc}x&10&15&20&25&30&35&40\\C&4425&2950&2212.5&1770&1475&1264.29&1106.25\end{array}\right] [/tex]
[tex] \left[\begin{array}{cccccccc}\\dC/dx&-442.5&-196.67&-110.635&-70.8&-49.17&-36.12&-27.66\end{array}\right] [/tex]
The driver who gets 15 mpg would benefit more because
(-44250/16)/16 = -172.85
(-44250/36)/36 = -34.14
The driver with 15 mpg saves much more money than the driver with 35 mpg.
Once again, not fully certain if that is correct, but the answer seems logical to me, and I did google a bit to check it.
