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The fuel economy of a car, measured in the miles per gallon, is modeled by the function f(s)= -0.0009s^2+ 0.699s+12 where s represents the average speed of the car, measured in miles per hour. What average speed results in the maximum fuel economy?

A. -38.83 miles per hour
B. 38.83 miles per hour
C. 3.88 miles per hour
D. 25.57 miles per hour

Respuesta :

we are given

[tex]f(s)=-0.0009s^2+0.699s+12[/tex]

where

s represents the average speed of the car in miles per hour

For maximum fuel economy , we will have to find derivative of f(s)

and then we set it to 0

after that we can solve for s

[tex]f'(s)=-0.0009\times 2s+0.699+0[/tex]

[tex]f'(s)=-0.0018s+0.699[/tex]

now, we can set it to 0

and then we can solve for s

[tex]f'(s)=-0.0018s+0.699=0[/tex]

[tex]-0.0018s=-0.699[/tex]

[tex]s=\frac{0.699}{0.0018}[/tex]

[tex]s=388.333[/tex]mph....................Answer

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