# A Parabola Modelling Fuel Consumption

• Sep 17th 2011, 08:45 PM
Manni
A Parabola Modelling Fuel Consumption
A car consumes gas according to the equation f(v) = (v − 10)2 + 9900 where v is its speed in km/hr and f(v) is the fuel consumption rate in ml/hr. Find the speed that gives best fuel economy, i.e., the best distance-to-fuel ratio. Hint: The idea is to minimize fuel per unit distance, not per unit time.

Hey, I was just wondering how I would solve this problem without using Calculus. I approached it by graphing the f(v) and determining the minimum via the vertex form f(x) = (x-a)^2 + h. Are there any other methods?
• Sep 17th 2011, 09:30 PM
CaptainBlack
Re: A Parabola Modelling Fuel Consumption
Quote:

Originally Posted by Manni
A car consumes gas according to the equation f(v) = (v − 10)2 + 9900 where v is its speed in km/hr and f(v) is the fuel consumption rate in ml/hr. Find the speed that gives best fuel economy, i.e., the best distance-to-fuel ratio. Hint: The idea is to minimize fuel per unit distance, not per unit time.

Hey, I was just wondering how I would solve this problem without using Calculus. I approached it by graphing the f(v) and determining the minimum via the vertex form f(x) = (x-a)^2 + h. Are there any other methods?

Since \$\displaystyle (v-10)^2\$ is non-negative the minimum fuel consumption occurs when \$\displaystyle (v-10)=0\$

CB