Find derivative

Question

Based on data from a research​ group, a model for the total stopping distance of a moving car in terms of its speed is s=1.1v+0.077v2​,

where s is measured in ft and v in mph. The linear term 1.1v

models the distance the car travels during the time the driver perceives a need to stop until the brakes are​ applied, and the quadratic term 0.077v²

models the additional braking distance once they are applied. Find ds/dv at v=45 and v=80 mph, and interpret the meaning of the derivative.

Answer 1

s' = 1.1 + 0.154v

s'(45) = 1.1 + 0.154(45) = 8.08 feet per mph

s'(80) = 1.1 + 0.154(80) =13.42 feet per mph