Locate Any Relative Extrema and Inflection Points of the Function $y = x ^ { 6 } \ln \frac { x } { 6 }$

Multiple Choice

Locate any relative extrema and inflection points of the function $y = x ^ { 6 } \ln \frac { x } { 6 }$ .

A) relative minimum at $x = 6 e ^ { \frac { - 1 } { 6 } }$ ; inflection point at $x = 6 e ^ { \frac { - 11 } { 30 } }$
B) relative minimum at $x = 6 e ^ { \frac { - 1 } { 6 } }$ ; no inflection points
C) no relative maximum or minimum; inflection point at $x = 6 e ^ { \frac { - 1 } { 6 } }$
D) no relative extrema or inflection points.
E) relative maximum at $x = 6 e ^ { \frac { - 1 } { 6 } }$ ; inflection point at $x = 6 e ^ { \frac { - 11 } { 30 } }$