Locate Any Relative Extrema and Inflection Points of the Function $y = x \ln \frac { x ^ { 9 } } { 8 }$

Multiple Choice

Locate any relative extrema and inflection points of the function $y = x \ln \frac { x ^ { 9 } } { 8 }$ .

A) no relative extrema; inflection point at $x = 8 e ^ { \frac { - 17 } { 72 } }$
B) relative maximum at $x = \left( \frac { 8 } { e } \right) ^ { \frac { 1 } { 9 } }$ ; inflection point at $x = 8 e ^ { \frac { - 1 } { 9 } }$
C) relative minimum at $x = 8 e ^ { \frac { 1 } { 9 } }$ ; inflection point at $x = 8 e ^ { \frac { - 17 } { 72 } }$
D) no relative extrema; inflection point at $x = 8 e ^ { \frac { - 17 } { 72 } }$
E) relative minimum at $x = \left( \frac { 8 } { e } \right) ^ { \frac { 1 } { 9 } }$ ; no inflection points