In the formula c = 2r, c stands for

We can't tell.  Any certain letter doesn't have to mean the same thing wherever you see it.  You can use any letter you want to represent any quantity you want when you write an expression or a formula, as long as you clearly tell what it stands for.

C = 2r          This could mean anything.

It could mean that Julie has a great many pets.  For every rat she has,
she also has two cats.  Write a formula that tells how many cats she
needs for 16 rats.

It could mean that the Circumference of a circle is equal to 2 times
the length of the circle's radius.

It could mean that Rocko is baking oatmeal-raisin cookies.  He is
cutting each raisin in half, and putting 1/2 of one raisin in each cookie.
Write a formula that tells how many cookies he can make with 16 raisins.

Answer

1 number

explanation

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.