Identify the Open Intervals on Which the Function $y = 9 x - 18 \cos x , 0 < x < 2 \pi \text { is }$

question 5

Multiple Choice

Identify the open intervals on which the function $y = 9 x - 18 \cos x , 0 < x < 2 \pi \text { is }$ increasing or decreasing.

• A) increasing on \(\left( \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 } \right) ;\) decreasing on \(\left( 0 , \frac { 7 \pi } { 6 } \right)\) and \(\left( \frac { 11 \pi } { 6 } , 2 \pi \right)\)
• B) increasing on \(\left( 0 , \frac { 11 \pi } { 6 } \right)\) and \(\left( \frac { 7 \pi } { 6 } , 2 \pi \right)\); decreasing on \(\left( 0 , \frac { 7 \pi } { 6 } \right)\)
• C) increasing on \(\left( 0 , \frac { 7 \pi } { 6 } \right)\) and \(\left( \frac { 11 \pi } { 6 } , 2 \pi \right)\); decreasing on \(\left( \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 } \right)\)
• D) increasing on \(\left( 0 , \frac { 7 \pi } { 6 } \right)\) and \(\left( \frac { 5 \pi } { 6 } , 2 \pi \right)\); decreasing on \(\left( \frac { 7 \pi } { 6 } , \frac { 5 \pi } { 6 } \right)\)
• E) increasing on \(\left( \frac { 7 \pi } { 6 } , \frac { 5 \pi } { 6 } \right)\) and \(\left( \frac { 5 \pi } { 6 } , 2 \pi \right)\); decreasing on \(\left( \frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 } \right)\)

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Definitions:

Absolute Threshold

The minimum intensity of a stimulus that one can detect 50% of the time.

Subliminal

Below one’s absolute threshold for conscious awareness.

Adaptive

Describing an organism or system that can adjust to changes in its environment or circumstances.

Signal Detection Theory

A method for measuring the capacity to distinguish between patterns that carry information and those random patterns that obscure the information.