Gasoline Mileage From information given in a recent busi- ness publication, we constructed the mathematical model 1 M(x) = -x? + 2r – 20, 30 < x s 65, 45 to represent the miles per gallon used by a certain car at a speed of x mph. Find the absolute maximum miles per gallon and the absolute minimum and the speeds at which they occur.

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A: see below the answer and explanation