Acollector has 80 movie posters and 50 band posters. she wants to sell 40 movie posters but still have her poster collection maintain the same ratio of 80: 50. if she sells 40 movie posters, how many band posters should she sell? complete the explanation to find out how many band posters should she sell.

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.