Given z subscript 1 baseline equals 2 left-parenthesis cosine Start Fraction pi over 6 End Fraction plus i sine Start Fraction pi over 6 End Fraction right-parenthesis and z subscript 2 baseline equals 3 left-parenthesis cosine Start Fraction pi over 4 End Fraction plus i sine Start Fraction pi over 4 End Fraction right-parenthesis, find z subscript 1 baseline z subscript 2 baseline where 0 less-than-or-equal-to theta less-than 2 pi.

Step-by-step explanation:

1.42+n⋅2π

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.