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 consta

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?

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Khang Minh 5 months 2021-08-18T11:42:14+00:00 1 Answers 86 views 1

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    2021-08-18T11:44:06+00:00

    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.

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