Aclass of 260 students went on a field trip. they took 12 vehicles, some cars and some buses. find the number of cars and the number of buses they took if each car holds 5 students and each bus holds 25 students. let c= cars and b= buses.

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.