3time y = 15.3
select all the equations where x would have the same value as y
a) x/5.1 = 2
b) x/2 = 2.55
c) x/2.55 = 2
d) x/5.1 = 2.55

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.