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Answer

1 number

explanation

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.

step-by-step explanation:

when the line is solid:

it's either < or >

when the line is dashed:

it's either < or >

this > inequality sign means:

greater thanmore thanaboveexceeds

this < inequality sign means:

less thanfewer thanbelow

this > inequality sign means:

greater than/equal tono less thanat leastminimum of

this < inequality sign means:

less than/equal tono more thanat mostmaximum of

about the problem:

since the line is solid, that means it's either < or >

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The correct answer is 7