If it is a school night, eric goes to bed early. eric will not go to bed early tonight. therefore, it is not a school night. determine if the statement is valid. a. no, /, therefore,/ is an invalid argument. b. no, /, therefore, / is an invalid argument. c. yes, /, therefore, / is a valid argument. d. there is not enough information to determine.

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.