Title: Interpreting Derivatives Task
Course: Calculus I

Q: Courtney is going on a road trip. The function f(t) measures the amount of fuel Courney's car has consumed (in gallons) where t is measured in hours since Courtney has left her hometown. Which statement best explains the meaning of f ` ( 5 ) = 25?
- Five hours since Courtney left her hometown, Courtney's car has consumed 2.5 gallons of fuel. (Incorrect)
- Over the five hours since leaving her hometown, the amount of fuel consumed by Courtney's car will increase by 2.5 gallons over the next hour. (Incorrect)
- Five hours after Courtney left her hometown, the amount of fuel consumed by Courtney's car will increase by 2.5 gallons over the next hour. (Incorrect)
- As time increases by a very small amount from 5 hours, the amount of fuel consumed by Courtney's car increases by approximately 2.5 gallons over the next hour. (Correct)
- The instantaneous rate of change of the amount of fuel consumed with respect to time is 5. (Incorrect)
A: As time increases by a very small amount from 5 hours, the amount of fuel consumed by Courtney's car increases by approximately 2.5 gallons over the next hour.