Ana uses Talk-A-Lot and Peter uses Talk-to-Me. Each company charges the same amount per hour of talk time, however Ana and Peter will never
be charged the same amount. Write a system of equations that could
represent the situation. Explain.

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.

35-60 students are taking math.