Answer
a) $f'(x)$ is negative.
b) The unit of $f'(x)$ is mpg/pound or miles per gallon per pound.
Work Step by Step
Let $x$ be the amount of weight (in pounds) loaded and $y$ be the mileage (in mpg).
It is given that as more weight is added, the mileage goes down. This means that as $x$ increases $f(x)$ decreases. $f(x)$ decreases if and only if $f'(x)<0.$ Therefore, $f'(x)$ is negative.
The derivative is the rate of change of $y$, i.e. mileage (in mpg), with respect to $x$, the weights added (in pounds). Hence the unit of $f'(x)$ is mpg/pound.
