The coach for the cheerleaders is shopping for uniforms for eight new
cheerleaders.
Sports Discount is offering a 20%
discount on each uniform. Each
uniform is priced at $68.00. A 7%
sales tax will be applied to the
discounted price.
The same uniforms are also available
on Cheerleading for Less web site for
$56.50. The tax on the uniforms is
8.5% plus a total shipping fee of
$29.99 for the entire order.
What is the difference in the total
costs of the 8 new uniforms between
the two stores?

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.