A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 7 cents per minute of use. In Plan B, the customer pays a monthly fee of $9.80 and then an additional 5 cents per minute of use. For what amounts of monthly phone use will Plan A cost more than Plan B?
Use m for the number of minutes of phone use in a month, and solve your inequality for m.

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Step-by-step explanation:

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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.