Select the postulate that is illustrated for the real numbers

5 + (-5) = 0

a. the commutative postulate for multiplication

b. multiplication by one

c. the addition inverse postulate

d. commutative postulate for addition

e. the distributive postulate

f. the addition of zero postulate

g. the multiplication inverse

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.