Provide an Appropriate Response $f ( x ) = \ln ( \sin x )$

question 282

Multiple Choice

Provide an appropriate response.
-Find the absolute maximum and minimum values of $f ( x ) = \ln ( \sin x )$ on $\left[ \frac { \pi } { 6 } , \frac { 2 \pi } { 3 } \right]$ .

• A) Maximum \(= 0\) at \(x = 0\), minimum \(= - \ln 2\) at \(x = \frac { \pi } { 6 }\)
• B) Maximum \(= 0\) at \(x = \frac { \pi } { 2 }\), minimum \(= \ln \frac { \sqrt { 3 } } { 2 }\) at \(x = \frac { 2 \pi } { 3 }\)
• C) Maximum \(= 0\) at \(x = \frac { \pi } { 2 }\), minimum \(= - \ln 2\) at \(x = \frac { \pi } { 6 }\)
• D) Maximum \(= 0\) at \(x = \frac { \pi } { 2 }\), minimum \(= - \ln 2\) at \(x = \frac { 2 \pi } { 3 }\)

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