Question

2) For a car driven 100 kilometers at a constant speed, the amount of fuel used as a function of the speed is modeled by a differentiable function F. Fuel is measured in liters, and speed is measured in kilometers per hour (km/hr). In this context, which of the following is a correct interpretation of the statement F

′
(50)>F
′
(80) ? a) Driving at 50 km/hr uses more fuel than driving at 80 km/hr. b) The rate at which 50 liters of fuel is used is greater than the rate at which 80 liters of fuel is used. d) The rate of change of liters of fuel used with respect to the speed is greater when driving at 50 km/hr than when driving at 80 km/hr

Answer 1

The statement F'(50) > F'(80) means that the sensitivity of fuel consumption to changes in speed is greater at 50 km/hr than at 80 km/hr, not that more fuel is used at one speed over the other.

Step-by-step explanation:

The correct interpretation of the statement F ′(50) > F ′(80) in the context of the amount of fuel used as a function of the speed is option (d): The rate of change of liters of fuel used with respect to the speed is greater when driving at 50 km/hr than when driving at 80 km/hr.

This means that when the car's speed increases slightly from 50 km/hr, the rate at which the fuel consumption is increasing is greater than the rate at which it would increase if the car's speed were increasing slightly from 80 km/hr. It is important to understand that this statement does not compare the actual amount of fuel used at these speeds but rather the sensitivity of the fuel consumption to changes in speed at these two points.