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

Multiple Choice

Locate any relative extrema and inflection points of the function $y = \frac { x ^ { 8 } } { 8 } - \ln x$ . Use a graphing utility to confirm your results.

A) relative maximum value $y = \frac { 1 } { 8 }$ at $x = 1$ ; inflection point at x = 0
B) relative minimum value $y = 8$ at $x = 1$ ; inflection point at x = 0
C) relative minimum value $y = 8$ at $x = 1$ ; no inflection points
D) relative minimum value $y = \frac { 1 } { 8 }$ at $x = 1$ ; no inflection points
E) relative maximum value $y = \frac { 1 } { 8 }$ at $x = 1$ ; no inflection points