Mason is driving on a long road trip. He currently has 12 gallons of gas in his car. Each hour that he drives, his car uses up 1.5 gallons of gas. How much gas would be in the tank after driving for 2 hours? How much gas would be left after tt hours?

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.