-4j - 1 - 4j + 6 in simplest form

-8j      +5

Step-by-step explanation:

-4j - 1 - 4j + 6

Combine like terms

-4j   -4j   -1 +6

-8j      +5

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.