Bob will rent a car for the weekend. He can choose one of two plans. The first plan has an Initial fee of $60 and costs an additional $0.50 per mile driven. The second plan has no initial fee but costs $0.70 per mile driven. How many miles would Bob need to drive for the two plans to cost the same?

Step-by-step explanation:

+55+%2B+.5x+=+.7x+

+.2x+=+55+

+x+=+275+

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.