HELP PLEASE, IM BEGGING YOU

1. -30/7

2. 5/2

3. 1 2/3

4. -3 2/5

5. 2 1/2 and -2 1/2

6. No values have an absolute value of -6 1/3 because the absolute value of a number is always positive

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.