Find the Exact Location of All the Relative and Absolute $( 0 , \infty )$

question 60

Multiple Choice

Find the exact location of all the relative and absolute extrema of the function with domain $( 0 , \infty )$ . $f ( x ) = x \ln \left( x ^ { 3 } \right)$

• A) \(\left( \frac { 1 } { e } , \frac { 3 } { e } \right)\) - absolute minimum
• B) \(\left( \frac { 1 } { e } , - \frac { 3 } { e } \right)\) - relative maximum
• C) \(\left( \frac { 3 } { e } , - \frac { 1 } { 3 e } \right)\) - absolute minimum
• D) \(\left( \frac { 1 } { e } , - \frac { 1 } { 3 e } \right)\) - relative minimum
• E) \(\left( \frac { 1 } { e } , - \frac { 3 } { e } \right)\) - absolute minimum