Manufacturers often advertise the miles per gallon, or mpg, for the cars they make. This measurement is a special kind of rate called a unit rate, because it is the mileage for one unit (one gallon) of gasoline. Calculate the unit rate (mpg) for each car in problem 7-24. List the cars in order from highest mpg to lowest. Explain how you made this calculation.

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step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.