The sum of two integers with different signs is 8. give two
possible integers that fit this description.

The sum of 2 integers with different signs is 8...
-1 + 9 = 8
-2 + 10 = 8
-3 + 11 = 8
-4 + 12 = 8
-5 + 13 = 8
-6 + 14 = 8
I could go on for a while

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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.