Chapter 4.4, Problem 79E

Fuel Economy (You saw this exercise in Section 4.3. This time, use the chain rule to calculate the derivative.) Your muscle car’s gas mileage (in miles per gallon) is given as a function $M\left(x\right)$ of speed x in miles per hour, where

$M\left(x\right)=\frac{3,000}{x+3,600x^{-1}}.$

Calculate $M\text{'}\left(x\right)$ and then $M\text{'}\left(10\right),M\text{'}\left(60\right)\text{, and }M\text{'}\left(70\right)$. What do the answer tell you about your car?