Determine the X-Coordinate(s) of Any Relative Extrema and Inflection Points $y = x ^ { 5 } \ln \frac { x } { 9 }$

Multiple Choice

Determine the x-coordinate(s) of any relative extrema and inflection points of the function $y = x ^ { 5 } \ln \frac { x } { 9 }$

A) relative minimum: $x = 9 e ^ { \frac { - 1 } { 5 } }$ ; no inflection points
B) relative maximum: $x = 9 e ^ { \frac { - 1 } { 5 } } ;$ inflection point: $x = 9 e ^ { \frac { - 9 } { 20 } }$
C) no relative maximum or minimum; inflection point: $x = 9 e ^ { \frac { - 1 } { 5 } }$
D) no relative extrema or inflection points.
E) relative minimum: $x = 9 e ^ { \frac { - 1 } { 5 } } ;$ inflection point: $x = 9 e ^ { \frac { - 9 } { 20 } }$