Question

The cost, C, in dollars, of fuel per month for Sanjay to operate his truck is given by C(v) = 0.0029v^2 - 0.48v + 142, where v represents his average driving speed in kilometres per hour. Find the most efficient speed at which Sanjay should drive his truck.

Answer 1

The way I read this, the "most efficient speed" means the speed the makes Sanjay's cost the lowest. Since the cost is expressed as a function of average speed, C(v), then you can find the minimum cost C by differentiating the function with respect to v. In other words, find the first derivative.

When you have the expression for the first derivative, you need to set that expression equal to zero... the "v" value that makes the first derivative equal zero is the most efficient average speed.