Answer:
[tex]v=\sqrt{\frac{b}{a}}[/tex]
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):
[tex]g(v)=av+\frac{b}{v}[/tex] (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:
[tex]\frac{dg(v)}{dv}=a-\frac{b}{v^2}[/tex] (2)
Next, you equal the previous result to zero and solve for v:
[tex]a-\frac{b}{v^2}=0\\\\v=\sqrt{\frac{b}{a}}[/tex]
For this value of v the fuel consumption is minimized.
