A small business selects a fixed amount of people each month to win a free T-shirt. The business had all the T-shirts made at the beginning of the year. On the graph shown, the variable y represents the number of free T-shirts remaining after x months. Which of the following situations is represented by the graph?

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.