The gas milage (in miles per gallon) of a subcompactcar is approximately, g(x) =

Question

The gas milage (in miles per gallon) of a subcompactcar is approximately,

g(x) = -15x^2 + 1125x / x^2 - 110x +3500

where x is the speed in miles per hour for (xgreater than or equal to35 and less than or equal to 65)

a.) Find g'(x)

b.) FInd g'(40), g'(50), and g'(60) and interpret your answers

c.) what does the change in sign of g'(40) tell you about wether gas mileage increases or decreases with speed when driving 40 mph? Do the same for g'(60) and 60 mph. Then do the same for g'(50) and 50 mph. From your answers, what do you think is the most economical speed for a compact car?

Explanation / Answer

g'(x) =(x^2-110x+3500)(-30x + 1125) -(-15x^2+1125x) ( 2x-110) / (x^2-110x+3500)^2 =-30^3+3300x^2-105000x+3937500+1125x^2-123750x+30x^3-2250x^2-1650x^2+123750x /(x^2-110x+3500) =525x^2-10500x+3937500 /(x^2-110x+3500) substitute the respective values and compute for example g'(40) substitute x=40

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