Drag the tiles to the correct boxes to complete the pairs. Sam works as a baggage carrier at an airport facility. He owes a certain amount of money, in dollars, to his friend Daniel. The function y = 12x − 40 represents the amount of money that Sam has after paying Daniel back in terms of the number of hours he works at the airport. Match the values and variables to the aspects of the situation they represent.

answer is x<

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.