The fuel consumption c of Micheal's car ( measured in gallons per hour ) is a function of speed ( or velocity ) v of the car ( measured in miles per hour). Since he has owned the car for several years now, Micheal has determined through experimentation that this relationship is
c(v) = 50 + ( v - 30 )^2 / 20 , where 20 > or = v < or = 80. then number of gallons consumed per mile, g(v), is defined g(v) = c(v) / v.
- Find the velocity 20 < or = v < or = 80 that minimizes c.
- Find the velocity 20 < or = v < or = 80 that minimizes g.
- which velocity would you recommend that Micheal drives at in order to save as much money as possible? Briefly explain.