Match each inequality with the correct solution. u > 6 - 2
3 + 4 < u
u + 4 < 8
9 - 2 > u
Answers:
7 < u, 7 > u, u < 4, u > 4

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.

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