Zalia meets her friend at the science museum to see a special exhibition. the admission to the museum is $12.50 plus tax. zalia pays for herself and her friend. they have lunch at the museum’s cafe. zalia has a sandwich for $5.95, an apple for $1.25 and a drink for $1.69. she is charged tax and also tips her server 15%. if tax is 7.25%, how much did zalia pay all total for her day at the science museum?

the slope of the first function is -3. (3/1)

the slope of the second function is 1. (13-10/6-3).

since |-3| is greater than |1|, the function with the steepest slope is the first.

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.