Question

A truck uses gas as g(v)=av+bv, where v represents the speed of the truck, g represents the gallons of fuel per mile, and a and b are constants. At what speed is fuel consumption minimized?

Answer 1

Answer:

$v=\sqrt{\frac{b}{a}}$

Explanation:

The correct statement is:

A truck uses gas as g(v)=av+b/v, where v represents the speed of the truck and g represents the gallons of fuel per mile. At what speed is fuel consumption minimized?

You have the following function g(v):

$g(v)=av+\frac{b}{v}$           (1)

g: gallons of fuel per mile

v: speed of the truck

In order to calculate the speed of the truck, you first calculate the derivative of the g(v) respect to v:

$\frac{dg(v)}{dv}=a-\frac{b}{v^2}$           (2)

Next, you equal the previous result to zero and solve for v:

$a-\frac{b}{v^2}=0\\\\v=\sqrt{\frac{b}{a}}$

For this value of v the fuel consumption is minimized.