3 connecting lines are shown. Line A B is horizontal. Line A C is about half the length of A B. Line B C is about one-third of the length of A B. Which inequality can be used to explain why these three segments cannot be used to construct a triangle?

AC + AB > CB
AC + CB < AB
AC + CB > AB
AC + AB < CB

AC + CB < AB

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.