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: