define g (v) to be the fuel efficiency in miles per gallon of a vehicle moving at v miles per hour. What are the units of g' (90) ? What does it mean in 'real world' terms if g' (55) = - 0.54?

... ?

By "g' (v) ", I presume you mean dg (v) / dv. If so, then the units of g' are (miles per gallon) / (miles per hour), and g' expresses the sensitivity of fuel consumption to vehicle speed. g' (55) = - 0.54 means that if a vehicle traveling at 55 miles per hour accelerates to an incrementally higher speed, the subsequent steady state mileage will decrease by a proportionality factor of 0.54.

lim delta y / delta x - > dy/dx as delta x - >0. so then dy/dx * delta x, where delta x = 1, we havedy ~ dy