Express the fractions 1/2, 3/16, and 7/8 with an lcda.8/16 3/16 14/16b. 1/4 3/4 7/4c. 1/32 3/32 732d. 4/8 6/8 14/8

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.