Homework Soursethe fuel consumption of an automobile is not constant fuel e
the fuel consumption of an automobile is not constant. fuel economy depends largely on the speed of the vehicle. the function f(v)=(8v^3)/(19125)+(28v^2)/(85)-(288v)/(85)+80 (F(v) is in miles per gallon, describes the fuel consumption of a new hybrid vehicle, where 0<v<85 is the velocity of the vehicle. on what intervals is the consumption increasing? which velocities yield maximum efficiencies? (remeber, high efficiency means low consumption. give answers to the tenths place)
Solution
We can answer this by taking the derivative of the function: f\'(v) = -288/85+(56 v)/85+(8 v^2)/6375 Using the quadratic equation, we find that f\'(v) = 0 at v = 5.09344 and here it changes from negative to positive. Therefore, we conclude that the consumption is increasing on the interval 5.09344 <= v < 85 Further, the maximum efficiency occurs at the minimum of f(v). We therefore conclude that v = 5.09344 is a minimum value of f(v) since f\'(v) = 0 here and changes from negative to positive. Thus, v = 5.09344 is the velocity yielding the maximum efficiency.
