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The gas mileage m(x) (in mpg) for a certain vehicle can be approximated by m(x) = -0.026x^2 + 2.593x - 35.023, where x is the speed of the vehicle in mph. What is the maximum/mph.

The gas mileage m(x) (in mpg) for a certain vehicle can be approximated by m(x) = -0.026x-example-1

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Answer:

To find the maximum gas mileage, we need to find the vertex of the parabola representing the gas mileage function.

The x-coordinate of the vertex of a parabola in the form of y = ax^2 + bx + c is given by -b/2a.

In this case, the gas mileage function is m(x) = -0.026x^2 + 2.593x - 35.023, so a = -0.026 and b = 2.593.

The x-coordinate of the vertex is therefore:

x = -b/2a = -2.593/(2*(-0.026)) = 49.9 (rounded to one decimal place)

This means that the maximum gas mileage occurs at a speed of 49.9 mph.

To find the maximum gas mileage, we can substitute x = 49.9 into the gas mileage function:

m(49.9) = -0.026(49.9)^2 + 2.593(49.9) - 35.023 ≈ 36.1 mpg

Therefore, the maximum gas mileage is approximately 36.1 mpg.

Explanation:

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