Determine the X-Coordinate(s) of Any Relative Extrema and Inflection Points $y = x \ln \frac { x ^ { 5 } } { 6 }$

Determine the x-coordinate(s) of any relative extrema and inflection points of the function $y = x \ln \frac { x ^ { 5 } } { 6 }$

A) relative minimum: $x = 6 e ^ { \frac { 1 } { 5 } } ;$ inflection point $: x = 6 ^ { \frac { - 9 } { 20 } }$
B) no relative extrema; inflection point: $x = 6 ^ { \frac { - 9 } { 20 } }$
C) relative minimum: $x = \frac { ( 6 ) ^ { \frac { 1 } { 5 } } } { e }$ ; no inflection points
D) no relative extrema; inflection point: $x = 6 e ^ { \frac { - 1 } { 5 } }$
E) relative maximum: $x = \left( \frac { 6 } { e } \right) ^ { \frac { 1 } { 5 } }$ inflection point: $x = 6 e ^ { \frac { - 1 } { 5 } }$